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Faculty of Applied Arts
October 6 University
LECTURES
IN
PHYSICS
For
First Year
Applied Arts Students
Second Term
Ast.Prof/Hala Moustafa Ahmed
LECTURES IN PHYSICS
Contents
CHAPTER (1): Physics Of Heat
1: Introduction.
2: Heat and Temperature.
2-1: Heat.
2-2:Temperature.
2-3:The human body temperature depends on.
2-4:The varies in temperature depend on.
3: Units of Heat.
4:Heat Capacity and Specific Heat.
5:Conservation of energy: calorimetry:
6:Latent Heat:
7: Heat Transfer.
7-1: Conduction.
7-2: Convection.
7-2-1:Types of convection methods.
7-2-1-A:In natural convection
7-2-2-B:Forced convection,
7-3: Radiation method.
7-4: Evaporation.
8:Examples of Good Conductors:
8-1:Examples of bad conductors:
9: Application of Convection Currents.
9-1: Refrigerators.
9-2:Hot water System:
9-3: Land and Sea Breezes:
10: Practical Application:
10-1: Electric water boiler.
10-2: Green House.
10-3: The vacuum flask.
10-4:House Insulation.
11:Thermodynamics
11-1:The thermodynamic system.
11-2:Types of energy of thermodynamic systems
11-2-1:Mechanical energy:
11-2-2: Heat and thermal energy:
11-2-3:Mechanical energy & heat or thermal energy:
12:Zeroth law of thermodynamics
12-1: Heat and internal energy:
12-2:Work and heat in thermodynamic processes:
13:The first law of thermodynamics.
14: Some applications of the first law of thermodynamics
15:Entropy
16:Second law of thermodynamics
17:Third law of thermodynamics
Solution of some selected problems
Story Problems
CHAPTER (2): Bioelectricity
1: Introduction.
2: Electric Field .
2-1: Electric Field Strength at Apoint .
2-2:Lines of Force.
2-3: Elecrical Potential Difference between Two Points.
2-4: Relation Between The Electric Field Strength and the Potential Difference.
3: Capacitors and capacitance.
3-1: The Capacitance.
3-1-1: The capacitance of parallel plate capacitor.
3-1-2: Series connection of capacitors.
3-1-3: Parallel connection of capacitors.
4: Energy stored in acapacitor.
5: Dielectric and dielectric constant.
6-1:Ohm's law .
6-2:The electrical resistance.
6-4:The electrical conductivity.
6-3: The electrical energy and power.
6-4:Temperature dependence of resistivity and resistance
7: Bioelectricity Within The Body
7-1:The cell membrane
7-2: Function.
7-3:Structure.
8:The nervous system and the neroun.
9:Membrane electrical potentials and nerve impulses
9-1:The propagation of action potential
9-1-1:The nerve conduction
10:The rsistance and capacitanc of membrane.
10-1:The capacitance of Membrane.
10-2:The resistance of an axon.
11:Direct current circuits:
11-1:Electromotive force (emf)
11-2:Ohm’s law circuits
11-2-1:For resistors in series
11-2-2:For resistors in parallel
12:Electric charge and magnetic field.
13:The radius of the circular path:r
14:The cathode ray oscilloscope (CRO)
15:The electrostatic deflection
16:Electrical Shocks
16-1:Electrical instruments used in medicine.
16-1-1:The electromyogram(EMG).
16-1-2:The electrocardiogram (ECG).
16-1-3:The electrooculogram (EOG).
Solution of some selected problems
Story Problems
References
BioPhysics & Physics Resources on the Web
Appendix
CHAPTER (1)
Physics Of Therapeutic Heat
Lesson Objectives:
By the end of this chapter, a student will be able to:
1-Explain the meaning of Heat transfer.
2-Explain Heat and Cold in Therapy.
3-Classify Heat methods
CHAPTER (1)
Physics Of Heat
1: Introduction.
Heat therapy is an increase in the metabolism resulting in a relaxation of the
capillary system.Heat therapy is an increase in the blood flow, as blood moves in to
cool the heated area. Heat can flow spontaneously from an object with a high
temperature to an object with a lower temperature. The transfer of heat from one
object to another object with an equal or higher temperature can happen only with the
aid of a heat pump. High temperature bodies, which often result in high rates of heat
transfer, can be created by chemical reactions (such as burning), nuclear reactions
(such as fusion taking place inside the Sun), electromagnetic dissipation (as in electric
stoves), or mechanical dissipation (such as friction).
2: Heat and Temperature.
2-1: Heat.
Heat is energy transferred from one body or system to another due to difference
in temperature (Q)
2-2:Temperature.
Temperature is aquantitative description of hotness and coldness of body.
2-3:The human body temperature depends on.
1-The amount of recent physical activity
2-The temperature of the environment
3-The health of individual
4-The clothes
2-4:The varies in temperature depend on.
1-The external physical
2-Circulation process near the skin
3-Blood flow near the skin
3: Units of Heat.
As a form of energy heat has the unit joule (J) in the International System of unit (SI).
However, in many applied fields in engineering the British Thermal Unit (BTU) and
the calorie are often used. The standard unit for the rate of heat transferred is the watt
(W), defined as joules per second.The total amount of energy transferred as heat is
conventionally written as Q for algebraic purposes.Heat released by a system into its
surroundings is by convention a negative quantity (Q < 0); when a system absorbs heat
from its surroundings, it is positive (Q > 0). Heat transfer rate, or heat flow per unit
time, is denoted by
.
Heat flux is defined as rate of heat transfer per unit cross-sectional area, resulting in
the unit watts per square metre.
4:Heat Capacity and Specific Heat.
Heat capacity (usually denoted by a capital C, often with subscripts), or thermal
capacity, is the measurable physical quantity that characterizes the amount of heat
required to change a substance's temperature by a given amount. In the International
System of Units (SI), heat capcity is expressed in units of joule(s) (J) per kelvin
(K).Temperature reflects the average total kinetic energy of particles in matter. Heat
is the transfer of thermal energy; it flows from regions of high temperature to regions
of low temperature. Thermal energy is stored as kinetic energy in the random modes
of translation in monatomic substances, and translations and rotations of polyatomic
molecules in gases. Additionally, some thermal energy may be stored as the potential
energy associated with higher-energy-modes of vibration, whenever they occur in
interatomic bonds in any substance. Translation, rotation, and the two types of energy
in vibration (kinetic and potential) represent the degrees of freedom of motion which
classically contribute to the heat capacity of a thermodynamic system. On a
microscopic scale, each particle in a system absorbs heat energy among the few
degrees of freedom available to it, and this absorption contributes to a specific heat
capacity which classically approaches a maximum per mole of particles that is set by
the Dulong-Petit law. The limit is achieved by many kinds of solids at room
temperature.For quantum mechanical reasons, at a given temperature, some of these
degrees of freedom may not be available, or only partially available, to store thermal
energy. In such cases, the specific heat capacity will be a fraction of the maximum. As
the temperature approaches absolute zero, the specific heat capacity of a system also
approaches zero, due to loss of available degrees of freedom. Quantum theory can be
used to quantitatively predict specific heat capacity in simple systems.An object's heat
capacity (symbol C) is defined as the ratio between the amount of heat energy
transferred to the object and the resulting increase in temperature of the object,
In the International System of Units, heat capacity has the unit joules per kelvin.
Heat capacity is an extensive property, meaning it is a physical property that scales
with the size of a physical system. A sample containing twice the amount of
substance as another sample requires twice the amount of transfer (Q) to achieve the
same change in temperature (ΔT). The specific heat c of a substance is the heat
capacity per unit mass.Thus, if Q units of thermal energy are transferred to m kg of a
substance, thereby changing its temperature by AT , the specific heat of the substance
is
from this definition, we can express the thermal energy Q transferred between a
substance of mass m and its surroundings for a temperature change AT as :
5:Conservation of energy: calorimetry:
Situations in which mechanical energy' is converted to thermal energy occur
frequently. We shall see some in the examples following this section and in the
problems at the end of the chapter, but most of out attention here will be directed
toward a particular kind of conservation of energy situation. In problems using the
procedure we shall describe, called calorimetry problems, only the thermal energy
transfer between the system and its surroundings is considered is considered.One
technique for measuring the specific heat of solids or liquids is simply to heat the
substance to some known temperature, and measure the temperature of the water after
aquarium is reached. Since a negligible amount of mechanical work is done in the
process, :the law of conservation of energy requires that the thermal energy that leaves
the wanner substance (of unknown specific heat) equals the thermal energy that
enters the eater. Devices in which this thermal energy transfer occurs are
called calorimeters.
For example, suppose that mx is the mass of a substance whose specific
heat we wish to determine, cx its specific heat, and Tx its initial temperature.
Likewise, let mw, cw and Tx represent corresponding values for the water. If T
is 3, we find that the thermal energy gained by the water is mw cw (T-Tw), and
the thermal energy lost by the substance of unknown c is - mx cx (T-Tx).
Assuming that the combined system (water + unknown) does not lose or
gain any thermal energy, it follows that thermal energy gained by the water
must equal the thermal energy lost by the unknown (conservation of energy):
Solving for cx gives
6:Latent Heat:
a substance usually undergoes a change in temperature when thermal energy is
transferred between the substance and its surroundings. There are situations, however
in which the transfer of thermal energy does not result in a change in temperature.
This is the case whenever the physical characteristics of the substance change from
one form to another, commonly referred to as a phase change. Some common phase
change are solid to liquid (melting), liquid to gas phase changes involve a change in
involve a change in internal energy.The thermal energy required to change the
phase of a given mass, m, of a pure substance is
Where L is called the latent heat (“hidden” heat) of the substance and depends on
the nature of the phase change as well as on the properties of the substance.Latent
heat of fusion ,Lf, is the term used when the phase change is from solid to liquid
(“fuse” means to melt, to liquefy), and latent heat of vaporization, L v, is used when
the phase change is from liquid to gas (the liquid vaporizes).
Fig:(1). Latent Heat
7: Heat Transfer.
Heat transfer is the passage of thermal energy from a hot to a colder body.
When a physical body, e.g. an object or fluid, is at a different temperature than its
surroundings or another body, transfer of thermal energy, also known as heat transfer,
or heat exchange, occurs in such a way that the body and the surroundings reach
thermal equilibrium. Heat transfer always occurs from a hot body to a cold one.
7-1: Conduction.
Conduction method is the transfer of thermal energy by molecular action
without any motion of the medium; it can occur in solids, liquids and gases .The
higher temperature molecules transfer some of their kinetic energy to the adjacent
molecules of low temperature size. Consider a block of a material with cross-sectional
area A and of length L, the temperatures at its two ends are T1&T2.The rate of heat
flow (Q/t) through this length is proportional to:

The area of the block (A).

The temperature difference (ΔT)

The time interval of flow (Δt)

Inversely proportional to the thickness (ΔX)
ΔQ = - KA ΔT
Δt
Δx
(J/m.s.ºC or watt/m.K)
Fig. (2): The rate of heat flow through the rod is proportional to Δt.L
Where: K is called coefficient of thermal conductivity and its unit is J/m.s.ºC or
watt/m.K.
The thermal conductivity (K) is defined as "the quantity of heat, Q, transmitted
in time (Δt) through a thickness (Δx), in a direction normal to a surface of area (A),
due to a temperature difference (ΔT) " Thermal conductivity is a material property that
is primarily dependent on the medium's phase, temperature, density, and molecular
bonding. The negative sign indicates the heat loss.
ΔQ = - KA ΔT
Δt
Δx
(J/m.s.ºC or watt/m.K)
7-2: Convection.
Convection is the transfer of thermal energy by fluid circulation or movement of
the hot particles in bulk to cooler areas in a material medium.
The thermal convection coefficient (Kc) is defined as "the quantity of heat, Q (lost or
gained) by a surface of area (A), in unit time (Δt) ,due to a temperature difference
(ΔT).
ΔQ = - Kc A (ΔT ) (J/m2.s.ºC or watt/m.K)
Δt
7-2-1:Types of convection methods.
7-2-1-A:In natural convection a fluid surrounding a heat source receives heat,
becomes less dense and rises. The surrounding, cooler fluid then moves
to replace it. This cooler fluid is then heated and the process continues, forming
convection current. The driving force for natural convection is buoyancy, a result of
differences in fluid density when gravity or any type of acceleration is present in the
system.
7-2-2-B:Forced convection, by contrast, occurs when pumps, fans or other means are
used to propel the fluid and create an artificially induced convection current. Forced
heat convection is sometimes referred to as heat advection, or sometimes simply
advection for short. But advection is a more general process, and in heat advection, the
substance being "advected" in the fluid field is simply heat (rather than mass, which is
the other natural component in such situations, as mass transfer and heat transfer share
generally the same equations).
7-3: Radiation method.
Radiation method is the transfer of heat through electromagnetic radiation. The
electromagnetic waves are of electric and magnetic origin ,it propaagates with
constant velocity equal 3x10 8 m/s.When the body is heated the viberating molecules
will emit electromagnetic waves,these waves when received by another body at lower
temperature will increase the thermal energy of its molecules,hence raiseits
temperature.Both reflectivity and emissivity of all bodies is wavelength dependent.
The temperature determines the wavelength distribution of the electromagnetic
radiation. All objects emit radiation .The rate Re at which radiant energy is emitted by
an object with surface area A and absolute temperature Te is
Re = ε σ A Te4
Where:
S is universal constant called Stephan Boltzman constant.S = 5.57x10-8 Watt/m2 K4
e is the emissivity varies between 0 and 1
The same object when placed closed area with wall at absolute temperature Ta will
absorb radiation energy from the walls at a rate
Ra = ε σ A Ta4
If the object is hotter than the walls, the net flow of energy from radiator to the walls
will be
R = Re – Ra
=
ε σ A (Te4 - Ta4)
7-4: Evaporation.
Evaporation is the transformation of molecules from liquid phase to thegaseous
phase.The amount of energy required to evaporate one mole of a liquid is called the
molar heat of vaporization (H).The molar heat of vaporization of water at 37 oC is 43.4
KJ.Since on mole of water 18g Then the energy necessary to vaporize each gram of
water is 43.4/18=2.4 KJ/g.
R=Q/t
Fig. (3): The 3 means of heat transmission: conduction, convection and radiation
8:Examples of Good Conductors:
All metals and alloys, and some non metals (e.g. graphite).
8-1:Examples of bad conductors:
Glass fibers, mineral wool, textiles, polyethylene, plastic foam, expanded
polystyrene containing tiny pockets of air enclosed inside, still air. Asbestos and
vacuum. Vacuum is the best thermal insulator followed by still air. Transmission of heat
through liquids: All ordinary liquids, with the exception of mercury and molten metal's,
are poor conductors. Never the less, they can transmit heat by other way called
convection. This can be shown by wrapping a piece of ice in gauge to make it sink and
place it at the bottom of a test tube nearly full of water by holding the top of the tube
in a Bunsen flame, the water at the top may be boiled vigorously while the ice at the
bottom remains un melted. Gases are far worse conductors of heat than liquids.
I) Conduction:
Based on the behavior of molecules, heat can be conducted from one place
to another by two ways:
i- Vibrating molecules:
When a molecule is heated and gain energy, it vibrates more and forces the
neighboring molecules to move apart and vibrate more. Hence heat is transmitted
from that molecule to others and so on. This process is a slow process for heat
transmition, so substances that conduct heat by this way are poor conductors of
heat.
ii- Free Electrons:
This process is characterized only for metals which have free electron cloud.
During the rapid rotation of the free electrons in the structure of the material, they
gain heat energy from the hot spot and dissipate it along their path to cooler spots.
This process is very efficient; therefore all metals are good conductors of heat.
II) Convection:
When a vessel containing a liquid is heated at the bottom a current of hot
liquid moves upwards and its place is taken by a cold current moving down wards.
This is due to the fact that when a portion of liquid near the bottom is heated it
expands. Since its mass remains the same, it becomes less dense, and therefore
rises. Thus a warm convection current moves upwards and cold convection current
moves downwards. This may be shown by filling a large spherical flask with water
and dropping a single large crystal of potassium permanganate to the bottom of it
through a length of glass tubing. On heating the bottom of the flask with a very
small gas flame, an upward current of colored water will ascend from the place
where the heat is supplied. This colored stream reaches the top and spreads out
after a short time it circulates down the sides of the flask, showing that convection
current has been set up. Gases also connect heat the same way as liquids.
Fig. (4): The heat transmission, convection
9: Application of Convection Currents.
9-1: Refrigerators.
Freezer units are used in households and in industry and commerce. Most freezers
operate around 0 °F (−18 °C). Domestic freezers can be included as a separate
compartment in a refrigerator, or can be a separate appliance. Domestic freezers are
generally upright units resembling refrigerators, or chests (resembling upright units
laid on their backs). Many upright modern freezers come with an ice dispenser built
into their door.
9-2:Hot water System:
The domestic hot water supply system consists of a boiler (A), a hot water storage
tank (B) and a cold supply tank (C) as shown. When the system is working a
convection current of hot water from the boiler rises up to the hot water tank (B) while
cold water descends to the boiler, where it becomes heated in turn. In this way
circulation is set up, with the result that the hot water storage tank gradually becomes
filled with hot water from the top downwards. Hot water to consumer is with-drawn
from the top of the hot water storage tank.
9-3: Land and Sea Breezes:
During the day the land is heated by the sun to a higher temperature than the sea.This is
because water has a higher specific heat capacity than earth and the surface of water is in
constant motion, leading to mixing of the warm surface water with the cooler layers below. Air
over the land is therefore heated, expands and rises while cooler air blows in from the sea.
Thus a breeze blows in from the sea. At night the land is cooler than the sea and the air
convection current is reversed.
10: Practical Application:
10-1: Electric water boiler.
An electric water boiler, also called an electric dispensing pot, electric water
heater, electric water urn, is a consumer electronics small appliance used for boiling
water and maintaining it at a constant temperature. It is typically used to provide an
immediate source of hot water for making tea, hot chocolate, coffee, instant noodles,
or baby formula, or for any other household use where clean hot water is required.
They are a common component of Japanese kitchens, but are found in varying use
globally.An electric water boiler consists of a water reservoir with a heating element at
the bottom. Some models offer multiple temperature settings. Other models are part of
larger water systems that boil water and provide hot, cold, and lukewarm water. Water
may be dispensed in various ways, e.g. by pouring, an electric pump or by pressing a
large button that functions as a diaphragm pump. Electric water boilers have a built in
thermostat that detects when water has reached its boiling point of 100 °C (212 °F) to
automatically shut off.
10-2: Green House.
The greenhouse effect is a process by which thermal radiation from a planetary
surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all
directions. Since part of this re-radiation is back towards the surface, energy is
transferred to the surface and the lower atmosphere. As a result, the temperature there
is higher than it would be if direct heating by solar radiation were the only warming
mechanism.
Fig.(5): Greenhouses and Greenhouse Plans
10-3: The vacuum flask.
It consists of a double - walled glass vessel having a vacuum between the
walls (to prevent heat exchange with the surrounding by conduction and
convection). Both walls are silvered on the vacuum side (to reduce heat
exchange by radiation). There will be a little heat transmitted by
conduction through the thin glass wall at the neck.
10-4:House Insulation.
A house may lose heat by the following ways
By conduction through the ceiling and roof.
By conduction through the windows.
By conduction through the floor.
By conduction through the walls.
By cold draughts and the escape of warm air.
Insulating the house is extremely necessary to save energy and minimize fuel bill. This
can be achieved by
Covering the roof with foam.
Using double glazing windows.
Placing a carbet on the floor
Using cavity filled double wall with plastic foam.
Making the windows air tight.
Fig(6):The theraiGgram of a home, made during cold weather, shows colons ranging from white and orange (areas of greatest energy loss) to blue and purple (areas of least energy loss.
11:Thermodynamics
11-1:The thermodynamic system.
It is any quantity of matter enclosed in some volume.
11-2:Types of energy of thermodynamic systems
11-2-1:Mechanical energy:
When molecules of the system have ordered motion, it is described by (Kinetic energy
and potential energy) which is usually resulting from application of an external force.
Energy:
It is the ability to do work.
Types of energy:
Kinetic Energy:
It is the energy gained by the body due to motion e.g(moving water,moving air).
Potential Energy:
It is the energy gained by the body due to position e.g(book on the shelf has more
energy than a book on the floor).
Heat Energy:
It is aform of energy that we can feel e.g (fire)
Light Energy:
It is aform of energy that we can see e.g (lamp ,tourch).
Sound Energy:
It is aform of energy that we can hear.sound moves in waves e.g (radio, drum).
11-2-2: Heat and thermal energy:
When molecules of the system have disordered or random motion, it is described by
thermal energy. The study of individual molecules in disordered motion is called heat.
11-2-3:Mechanical energy & heat or thermal energy:
When molecules of the system have disordered or random motion, as well as ordered
motion, it is described by the sum of thermal and mechanical energy.
12:Zeroth law of thermodynamics
It states that "when two systems A an B are in thermal equilibrium with a third system
C, then A anb are in thermal equilibrium.
12-1: Heat and internal energy:
When heat added to the system it causes the following:
i) Increase in internal energy, which appears as:
a. Increasing the translational energy of molecules which indicated by
an increase in temperature.
b. Increase in rotational energy of molecules.
c. Increase in vibrational energy of molecules.
d. Electronic excitation which may lead to ionization of atoms
ii) The system may expand.
iii) initiate the chemical reactions which lead to change the chemistry
and potential of the system.
i. It may accelerate the system and changes its kinetic energy.
12-2:Work and heat in thermodynamic processes:
in the macroscopic approach to thermodynamics we describe the state of a system
with such variables as pressure, volume , temperature, and internal energy.The
number of macroscopic variables needed to characterize a system depends on the
system’s nature. 'For a homogenous system, such as a gas containing only one type to
molecule, usually only two variables are needed. However, it is important to note that
a macroscopic state of an isolated system can be specific only if the system is in
thermal equilibrium internally. In the case of a gas in a container, internal thermal
equilibrium internally. In the case of a gas in a container, internal thermal equilibrium
requires that every part of the container be at the same pressure and temperature,
Consider gas contained in a cylinder fitted with a movable piston .
Fig.(7): Gas contained in a cylinder fitted with a movable piston
In equilibrium , the gas occupies a volume v and exerts a uniform pressure P on
the cylinder walls and piston. If the piston has a cross- sectional area A, the force
exerted by the gas on the piston is
F=PA
Now let us assume that the gas expands quasi-statically, that is, slowly enough
to allow the system to remain essentially in thermodynamic equilibrium at all
times.As the piston moves up a distance dy, the work done by the gas on the piston is
Since A dy is the increase in volume of the gas dV, we can express
the work done as
since the gas expands, dV is positive and the work done by the gas is positive,
whereas if the gas is compressed, dV in negative, indicating that the work done by the
gas is negative, (in the latter case, negative work can be interpreted as work being
done on the gas). Clearly, the work done by the gas is zero when the volume remains
constant. The total work done by the gas as its volume changes from Vi to V f is given
by the integral of equation
If the pressure and volume are known at each step of the process, the states of
the gas can then be represented as a curve on a PV diagram.
Fig.(8): Work = Area under curve
The work done in the expansion from the initial state to the final state is the
area under the curve in a PV diagram.work done by a system depends on the process
by which the system goes from the initial to the final state. In the other word, the work
done depends on the initial, final, and intermediate states of the system. In the similar
manner, the thermal energy transferred into or out of the system also depends on the
process. This can be demonstrated by considering the situations depicted in figure (8).
In each case, the gas has the same initial volume, temperature, and pressure and
is assumed to be ideal. In figure (8a), the gas is in thermal contact with a heat
reservoir. If the pressure of the gas is infinitesimally greater than atmospheric
pressure, the gas, because it absorbs thermal energy, expands and causes the piston to
rise. During this expansion to some final volume Vf, just enough thermal energy to
maintain a constant temperature Tj is transferred from the reservoir to the gas.
Fig.(9): Work and heat in thermodynamic processes
Now consider the thermally insulated system shown in figure (8b).When the
membrane is broken, the gas expands rapidly into the vacuum until it occupies a
volume VF and is at a pressure Pf in this case, the gas does no work because there is
no movable piston. Further more, no thermal energy is transferred thorough the
insulating wall. The initial and final states of the ideal gas in figure (8a) are identical
to the initial and final states in figure (8b), but the paths are different. In the first case,
thermal energy is transferred slowly to the gas, and the gas does work on the piston. In
the second case, no thermal energy is transferred and the work done is zero.
Therefore, we conclude that thermal energy transfer, like the work done, depends on
the initial, final and work depend on the path, neither quantity is determined by the
end
pints
of
a
thermodynamic
process.
13:The first law of thermodynamics.
When the law of conservation of energy was introduced in it was stated what the
mechanical energy of a system is constant in the absence of non-conservative forces
such as friction. That is the changes in the internal energy of the system were not
included in this mechanical model. The first law of thermodynamics, which we
discuss in this section is a generalization known as the law of conservation of energy
and encompasses possible changes in internal energy. It is a universally valid law that
can be applied to all kinds of process. Furthermore, it provides us with a connection
between the microscopic and macroscopic words.
We have seen that energy can be transferred between a system and its surroundings
in two ways. One is work done by (or on) the system, which requires that there be a
macroscopic displacement of the point of application of a force (or pressure).The other
is thermal energy transfer, which occurs through random molecular collisions. Each of
these represents a change of energy of the system and, therefore, usually results in
measurable changes in the macroscopic variables of the system, such as pressure,
temperature, and volume of gas.
To put these ideas on a more quantitative basis, suppose a thermodynamic
system undergo a change from an initial state tofinal state. During this change,
positive Q is the thermal energy transferred to the system, the positive W is the work
done by the system. As an example, suppose the system is a as whose pressure and
volume change from pi, v* to pf, vf. if the quantity Q -W is measured form caries
paths connecting the inlaid and final equilibrium states (that is , for carious prices), we
find that Q-W is the same for all paths connecting the initial and final states. We
conclude that the quantity Q-W is determined completely by the initial and final states
of the system, and we call the quantity Q-W the change in the energy of the system.
Although Q and W both depend on the path, the quantity Q-W is independent on the
path. If we represent the energy function with the letter U, then the change is energy.
Where all quantities must have the same energy units. Equation is known as
the first-law equation and is a key equation to many applications. When it is used in
this form, we use the convention that Q is positive when thermal energy enters the
system and negative when thermal energy leaves the system. Likewise, W is positive
when the system does work on the surroundings and negative if work is done on the
system.
Let us look at some special cases in which the only changes in energy are
changes in internal energy.First consider an isolated system, that is, one that does not
interact with its surroundings, in this case, no thermal energy transfer takes places and
the work done is zero; the internal energy remains constant. That is, since Q= w= 0,
and so Ui = Uf, we conclude that the internal energy of an isolated system remains
constant.Next consider a process in which a system (one not isolated from its
surrounding) is taken through a cyclic process, that is, one that originates and ends at
the same state. In this case the change is the internal energy must again be zero and,
therefore, the thermal energy added to the system must equal the work done during
the cycle. That is, in a cyclic process,
Note that the network done per cycle equals the area enclosed by the path
representing the process on a PV diagram.If a process occurs in which the work done
is zero, then the change in internal energy equal the thermal energy entering or
leaving the system. If thermal energy equal the thermal energy entering or leaving the
system. Q is positive and the internal energy increases. For a gas we can associate this
increase in internal energy with an increase in the kinetic energy of the molecules. On
the other hand, if a process occurs in which the thermal energy of the molecules. On
the other hand, if a process occurs in which the thermal energy transferred is zero and
work is done by the system, then the magnitude of the change in internal energy
equals the negative of the work done by the system. That is, the internal energy of the
system decreases, for example, if a gas is compressed with no thermal energy
transferred (by a moving piston, for example), the work done by the gas is negative
and the internal energy again increases. This is because kinetic energy in transferred
from
the
moving
piston
to
the
gas
molecules.
14: Some applications of the first law of thermodynamics
In order to apply the first law of thermodynamic to specific systems, it is useful
to first define some common thermodynamic processes:
I) Adiabatic process:
An adiabatic is one during which no thermal energy enters or leaves the system,
that is, Q=0. An adiabatic process can be achieved either by thermally insulating the
system from its surroundings or by performing the process rapidly applying the first
law of thermodynamic to an adiabatic process, we see that
ΔU=-W
from this results we see that if a gas expands adiabatically, w is positive, so ΔU
is negative and the temperature of the gas decreases. Conversely, the gas temperature
rises when it is compressed adiabatically.Adiabatic processes are very important in
engineering practice. Some common example include the expansion of hot gases in an
internal combustion engine, the liquefaction of gas in a cooling system, and the
compression stroke in a diesel engine.
II) Isobaric process:
A process that occurs at constant pressure is called an isobaric process. When
such a process occurs, the thermal energy transferred and the work done are both
usually non-zero. The wor£ done is simply
III) Isovolumetric process:
A process that takes place at constant volume is called in isovolumetric
process. In such an expansion process, the work done is clearly zero. Hence, from the
first law we see that in an isovolumetric process with W= 0.
ΔU= Q
This tells that if thermal energy is added to a system kept at constant volume,
all of the thermal energy goes into increasing the internal energy of the system. When
a mixture of gasoline vapor and air explodes in the cylinder of an engine, the
temperature and pressure rise suddenly because the cylinder volume doesn’t change
appreciably during the short duration of the explosion.
V-Isothermal process:
A process that occurs at constant temperature is called an isothermal process,
and a plot of p versus v at constant temperature for an ideal gas yields a hyperbolic
curve called an isotherm. The internal energy of an ideal gas is a function of
temperature only. Hence, in an isothermal process of an ideal gas.
ΔU= 0
15:Entropy
It is a measure of molecular disorder, as the disorder increases the entropy
increases. When a system is given a quantity of heat ΔQ at temperature T, the change
in entropy of this system is given by:
ΔS=Δ/T
16:Second law of thermodynamics
When two bodies at different temperature are in contact, heat always flows
from body of high temperature to body of law temperature.
17:Third law of thermodynamics
It is impossible to reach the absolute zero of temperature in any.
Solution of some selected problems
Example (1) :
A person walking at a modest speed generates heat,at a rate of 280 watt.If the
surface area of the body is 1.5m2.If the heat is assumed ti be generated 0.03 m
below the skin,what is the temperature differene between the skin and the
interior of the body would exist if the heat were conducted to the surface and
K=0.2 watt/m.K?
K=0.2 watt/m. ºK
A = 1.5m2
Δx = 0.03 m
ΔQ = 280 watt
ΔQ = - KA ΔT
Δt
Δx
(J/m.s.ºC or watt/m. ºK)
ΔT =ΔQ Δx =280x 0.03
= 28 ºK
Δt KA
0.2x1.5
Example (2):
In a warm room anaked resting person has a skin temperature of 33ºC.If the
room temperature is 29ºC and the body surface area is 1.5 m2 .What is the rate of
heat loss due to conection if kc =7.1 watt/ m2 .K?
kc =7.1 watt/ m2 .K
A = 1.5 m2
T2 = 33 ºC
T1 = 29 ºC
ΔQ = - KcA (ΔT ) (J/m2.s.ºC or watt/m.K)
Δt
= 7.1x1.5(33-29)= 43 watt
Example (3):
The skin temperature of anude person sitting in aroom at 20 oC is 30 oC.What is
the net rate of heat loss by radiation from the person body if the total surface
area of the body is 1.8m2? Emissivity of human in the infrared is 0.97, σ =
5.67x10-8 Watt/m2 K4 .
ε = 0.97
σ = 5.67x10-8 Watt/m2 K4
A = 1.8 m2
Te = 30 oC
Ta = 20 oC
R= ε σ A (Te4 -Ta4)
R = (0.97) (5.67x10-8W/m2K4)[(273+30)4 (273+20)4]
R =159.3 W
Example (4):
What is the rate of heat loss by radiation if a person has an area of 1.2 m2 and is
exchanging radiant energy with the environment of temperature 25 ºC if the skin
temperature is 33ºC , σ = 5.67x10-8 Watt/m2 K4and e = 1?
ε =1
σ = 5.67x10-8 Watt/m2 K4
A = 1.2 m2
Te = 33 oC
Ta = 25 oC
R= ε σ A (Te4 -Ta4)
R =1x5.67x 10-8 x 1.2(273+33) 4-(273+25)4 =59.9 J/s
Example (5) :
In the absence of any noticeable prespiration, there is an insensible evaporation
of water from the skin and lungs of the human body which amounts to 600 b of
water per day.What is the rate of heatloss due to insensible evaporation?
Q = 600 x 2.4 KJ/g = 1.44x103 KJ
R = Q/t
R = 1.44x103 KJ = 17 W
24x60x60
Example (6)
A student eats a dinner rated at 2000 (food) calories. He wishes to do an
equivalent amount of work in the gymnasium by lifting a 50.0 kg mass. How
many times must he raise the mass to expend this much energy? Assume that he
raises it a distance of 2.00 m each time and that he regains no energy when it is
droppec) to the floor.
Since 1 calorie = 1.00 x 103 cal. The work required is 2.00 x I06 cal.
Converting this to J, we have for the total work required.
W = (2.00 X 106 cal) (4.186/cal) = 8.37 x 106 J
The work done in lifting the mass a distance h is equal to mgh, and
the work done in lifting it n times is nmgh. We equate this to the total
work required:
W = nmgh = 8.37 x 106 J
8.37X106 J
N = ‫ = ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬8.54X10 times
(50.0kg) (9.80ml s2)(2.00m)
The student is in good shape and lifts the weight once every 5 s, it will take him
about 12 h to perform this feat. Clearly, it is much easier to lose weight by
dieting.
Example (7):
A 0.0500-kg ingot of metal is heated to 200.0 °C and then dropped into a
beaker containing 0.400 kg of water initially at 20.0 °C.If the final equilibrium
temperature of the mixed system is 22.4 °C, find the specific heat of the metal.
Because the thermal energy lost by the ingot equals the thermal energy gained by
the water, we can write:
(0.0500kg) (cx) (200.0 °C -22.4 C°) = (0.400 kg) (4186 j/kg. °C) (22.4 C° 20.0 °C ) from which we find that
cx = 453 j/kg. °C
Example (8):
A man fires a silver bullet of mass 2.00 g with a muzzle speed of 200 m/s
into the pine wall of a saloon. Assume that all the internal energy generated by
the impact remains with the bullet. What is the temperature change of the
bullet?
The kinetic energy of the bullet is
Vi mv2 = >/2 (2.00 x 10'3 kg) (200 m/s)2 = 40.0 J
from
Q = me T
Example (9):
What mass of steam initially at 130 °C is needed to warm 200g of water in a
100-g glass container from 20.0 °C to 50.0 °C ?
Qi = ms cs AT
= ms (2.01x 103 J/kg °C) (30.0 °C)
= - ms (6.03x 104 J/kg)
Q = m Lv:
Q2 = - ms (2.26x 106 J/kg)
Q3 = ms cw AT
= ms (4.19x 103 J/kg °C) (50.0 °C)
= - ms (2.09x 105 J/kg)
Qhot = Q1+Q2+Q3
= - ms (6.03x 104 J/kg) + ms (2.26x 106 J/kg)+ ms (2.09x 105
J/kg) = - ms(2.53xl06 J/kg)
Qcoid = (0.200 kg) (4.19x 103 J/kg °C) (30.0 °C) + (0.100 kg)
(837 J/kg °C) (30.0 °C).
Qcold = Qhot
2.77xl04 J = - [- ms(2.53xl06 J/kg) ]
ms = 1.09 x 10'2 J/kg = 10.9 g
Example (10):
One gram of water occupies a volume of 1.00 cm at atmospheric pressure. When
this amount of water is boiled, it becomes 1671 cm . calculate the change in
internal energy for this process.
Q= m Lv = (1.00 x 10'3 kg) (2.26 x 106 J/kg) = 2260 J- W = P
(Vv- V,)
= (1.013 x 10s N/m2) [(1671 - 1.00)x 10'6 m3] = 169 J AU = Q W = 2260 j -169 j = 2.09 Kj
Example (11):
A 1.0 kg bar of copper is heated at atmospheric pressure. If its
temperature increases from 20°C to 50°G,
(a) find the work done by the copper.
(b) what quantity of thermal energy is transferred to the copper?
(c) what is the increasing internal energy of the copper?
a-
β=3 α
Δv= β V ΔT =[5.bd0'5(oC)_1](50oC-20oC)V = 1.5x10“3V
Δv=1.5x10-3(1 kg/8.92x103 kg/m3)
Δv=1.7x10-7m3
w = p Δv= (1.013x 105 N/m2)( 1.7x1 O'7 m3)=1.9xlO'2J
b- Q = mcAT = (1.0kg) (387J/kg °C) (30°C)=1.2xl04J
c-AU = Q-W = 1.2xl04J
Story Problems
1-A person walking at a modest speed generates heat,at a rate of 110 watt.If the
surface area of the body is 1.6 m2.If the heat is assumed ti be generated 0.05 m
below the skin,what is the temperature differene between the skin and the
interior of the body would exist if the heat were conducted to the surface and
K=0.2 watt/m.K?
2-In a warm room anaked resting person has a skin temperature of 30ºC.If the
room temperature is 20ºC and the body surface area is 1.5 m2 .What is the rate of
heat loss due to conection if kc =7.1 watt/ m2 .K?
3-The skin temperature of anude person sitting in aroom at 24oC is 34 oC.What is
the net rate of heat loss by radiation from the person body if the total surface
area of the body is 1.8m2? Emissivity of human in the infrared is 0.97.
4-What is the rate of heat loss by radiation if a person has an area of 1.2 m 2 and
is exchanging radiant energy with the environment of temperature 25 ºC if the
skin temperature is 33ºC , S = 5.57x10-8 Watt/m2 K4and e = 1?
5-In the absence of any noticeable prespiration, there is an insensible evaporation
of water from the skin and lungs of the human body which amounts to 666b of
water per day.What is the rate of heatloss due to insensible evaporation?
6-A student eats a dinner rated at 2000 (food) calories. He wishes to do an
equivalent amount of work in the gymnasium by lifting a 50.0 kg mass. How
many times must he raise the mass to expend this much energy? Assume that he
raises it a distance of 2.00 m each time and that he regains no energy when it is
droppec) to the floor.
7-A 0.0500-kg ingot of metal is heated to 200.0 °C and then dropped into a
beaker containing 0.400 kg of water initially at 20.0 °C.If the final equilibrium
temperature of the mixed system is 22.4 °C, find the specific heat of the metal.
8-A man fires a silver bullet of mass 2.00 g with a muzzle speed of 200 m/s
into the pine wall of a saloon. Assume that all the internal energy generated
by the impact remains with the bullet. What is the temperature change of
the bullet?
2
9-What mass of steam initially at 130 °C is needed to warm 200g of water in a
100-g glass container from 20.0 °C to 50.0 °C ?
10-One gram of water occupies a volume of 1.00 cm at atmospheric pressure.
When this amount of water is boiled, it becomes 1671 cm . calculate the change in
internal energy for this process.
3
CHAPTER (2)
Bioelectricity
Lesson Objectives:
By the end of this chapter, a student will be able to :
1-Find Properties of bioelectricity.
2-Explain Electrical Potential Difference between Two Points
3-Conclude the rules for determining Capacitors and capacitance
4-Calculate Dielectric and dielectric constant
5-Prove the Bioelectricity within the Body
6-Examine Ohm's law
4
Chapter (2)
Bioelectricity
1: Introduction.
There are two aspects of electricity and magnitis in medicine.Electrical and
magnetic effects generated inside the body.Applications of electricity and magnitism
to the surface of the body.For example.The forces of muscles are caused by the
attraction and repulsion of electrical charges.The action of the brain is basically
electrical.All nerve signals to and from the brain involve the flow of electrical
currents.There are many electrical signals are generated from the body.These signals
are the result of the electrochemical action of certain of certain types of
cells.Measuring these signals (with out distribing the body ) we canobtain useful
clinical information about particular body functions .Some examples of these signals
are the electrical potentials of nerve transmission and the electrical signals of the
muscle the heart,and the brain.In order to understand and deal with these electrical
signals,we should study the fundmentals of electricity.
2: Electric Field .
It is defined as the space around the electric charge in which the electrical
effects appear.
2-1: Electric Field Strength at Apoint .
The electrical Field strength at the point is defined as the force per unit charge at
the point.Its SI unit is (N/C), electric field strength E is given by:
E=F/Q
(N/C)
5
Where:
F is the electric force experienced by the particle
q is its charge
E is the electric field wherein the particle is located
2-2:Lines of Force.
In order to visualize the electric field we consider the electric lines of
force.These are imaginary lines pointing outward from positive charge and inward to
the negative charge.
Fig: (10). Lines of Force
2-3: Elecrical Potential Difference between Two Points.
It is defined as the work done to move a positive unit charge from one point to
another If WAB is the work done to move a charge Q from point Ato point B,then the
potential difference V is given by:
VAB =
(J/C) or Volts
Potential difference can be measured with a voltmeter.Thus, the work done in
moving a charge Q between two points A and B in a potential difference V AB is given
by :
WAB =QVAB (J)
Note that whenever an electric charge is placed between two points having
potential difference there will be a work tending to move the charge from the point of
6
higher potential to the point of lower potential.Thus if the two points have the same
potential the work will be zero.The surface on which all points have the same potential
is called "equipotential surface"/Any charge on this surface will move freely.
2-4: Relation Between The Electric Field Strength and the Potential Difference.
The work done ΔW to move a charge Q against an electric field of strength E a
distance ΔX is given by:
ΔW=F ΔX
Where:
F is the electrostatic force and is given by:
F=QE
ΔW=QE ΔX
From the definition of the potential difference:
ΔV= ΔW = QEΔX=EΔX
Q
Q
E= ΔV
ΔX
(V/m)
3: Capacitors and capacitance.
Capacitor is a device that stores electrical energy .It consists simply of two
conductors charged by equal and opposite charges and separated by small
distance.One of the famous capacitors is the parallel plate capacitors in which the two
conductors are two parallel plates.
7
3-1: The Capacitance.
The capacitance of a capacitor is defined as the quotient of the charge on either
conductor to the potential difference between the conductors .Thus if Q is the charge
on the conductors of a capacitor and V the potential difference between the
conductors, the capacitance C is given by:
C = Q
V
(C/V) or Farad (F)
The farad (the unit of the capacitance) is a huge unit .In practice milli, nano, or
pico-farad is usually used
1 milli-Farad=1mF=103 F
1 nano-Farad=1nF=10-9 F
1 pico-Farad=1pF=10-12 F
3-1-1: The capacitance of parallel plate capacitor.
Consider aparallel plate capacitors with charge Q on its plates which separated
by a distance d and having an effective area A .The capacitance of this capacitor is
directly proportional to its area and inversely proportional the distance between the
plates.That is
C α A/d
or
C = ε0 A
d
Where:
εº is the permittivity of space
8
Fig: (11).Charge separation in a parallel-plate capacitor causes an internal electric field.
3-1-2: Series connection of capacitors.
When a group of capacitors of capacitances C1, C2, C3,…….are connected in
series ,their equivalent capacitanceC is given from
1 = 1 + 1
C
C1
C2
Fig:(12).Series connection of capacitors
3-1-3: Parallel connection of capacitors.
When a group of capacitors of capacitances C1, C2, C3,.are connected in parallel
,their equivalent capacitanceC is given from
C = C1 + C2+ C3
9
Fig:(13).Parallel connection of capacitors
4: Energy stored in acapacitor.
The energy stored in a capacitor is given by:
W = 1 QV = 1 CV2 = 1
2
2
2
Q2 (J)
2C
5: Dielectric and dielectric constant.
According to their electrical conductivity materials are classified into good
conductors, bad conductors (insulators) and semiconductors.Dielectric materials are
insulators.When an insulator material (dielectric) is placed between the plates of a
capacitor its capacitance increases.If C0 is the capacitance of parallel plat capacitor
when the gap between its plates is filled with air then its capacitance is given by:
C0 = ε0 A
d
Where:
ε0 is the permittivity of free space area A and d the distance.But when the gap is
filled with a dielectric material of permittivity ε its capacitance will be given by:
C=εA
d
From equations
C0 = ε0 A
d
01
and,
C = ε =K
C0
ε0
Where:
K is called the dielectric constant of the dielectric material and it is always
greater than one.Note that the capacitance C is greater than the capacitance C 0 by the
factor K.
6: Electric current intensity:
Electric current intensity is defined as the time rate of flow of electric charge
crossing any surface.When 1C of charge crosses a given surface in one second, a
current of 1 ampere (A) is flowing. When a charge Q crosses a surface in a time t y the
current I in amperes can be calculated with the following equation:
I = Q / t (C/s) or Ampere (A)
Where:
Q is the electric charge in coulombs (ampere seconds)
t is the time in seconds
When Q is in coulombs, and t is in seconds, i is in ampere.
Also we use the units of milli-ampere =10-3 A and microampere (MA) = 10'6A.
Fig:(14).Electric current intensity
00
6-1:Ohm's law .
Ohm's law states that :the current through a conductor between two points is directly
proportional to the potential difference .The mathematical equation that describes this
relationship is:
Vα I
V= IR
Where :
I is the current in amperes,
V is the potential difference in volts,
R is a circuit parameter called the resistance (measured in ohms, also equivalent
to volts per ampere).
Fig:(15).Ohm's law: I = V/R
6-2:The electrical resistance.
It is defined as the opposition of the flow of electric current.Its SI unit is the
ohm (Ω).
R = ρ
L
A
Where:
02
ρ is the resistivity of the material
L is the length
A is the cross sectional area
6-4:The electrical conductivity.
It is defined as the reciprocal of the resistivity.Its SI unit is (Ω -1 m-1)
σ = 1/ρ
6-3: The electrical energy and power.
When a quantity of charge Q passes between two points of potential difference V, the
electric energy carried by this charge is given by:
If the charge Q passes between the two points in a time (t), then Q = It. Where I
is the current passing between the two points. The electric energy is now given by
When V is measured in volts, i in amperes and t in seconds, the unit of W is joule.
Electric power
(9)
03
Another unit of electric power is the kilowatt-hour (KWh).
6-4:Temperature dependence of resistivity and resistance
The resistivity of most materials increases as its temperature increases. If ρ0 is
the resistivity of a material at an initial temperature T0 and p is its resistivity at higher
temperature T, the change in resistivity (ρ - ρ 0) is directly proportional to the change
in temperature (T-T0).
α: is a constant of the material, called the temperature coefficient of resistivity.
As the resistivity of conducting materials increases with Temperature, the resistance R
of these materials increases with temperature too. If RQ is the resistance of a material
at an initial temperature T0 and R is its resistance at higher temperature T, the change
in resistance (R-Ro) is directly proportional to the change in temperature (T-T0)
For all metals a= 1/273 per Celsius degree.
Fig:(16).Ohm's law: I = V/R
04
7: Bioelectricity Within The Body
7-1:The cell membrane
The cell membrane (also called the plasma membrane, plasmalemma,
or "phospholipid bilayer") is a selectively permeable lipid bilayer found in all
cells.It contains a wide variety of biological molecules, primarily proteins and
lipids, which are involved in a vast array of cellular processes such as cell
adhesion, ion channel conductance and cell signaling. The plasma membrane also
serves as the attachment point for both the intracellular cytoskeleton and, if
present, the cell wall.
Fig:(17).Illustration of a Eukaryotic cell membrane
7-2: Function.
The cell membrane surrounds the cytoplasm of a cell.The barrier is
selectively permeable.Able to regulate what enters and exits the cell, thus
facilitating the transport of materials needed for survival.The movement of
substances across the membrane can be either passive, occurring without the
input of cellular energy, or active, requiring the cell to expend energy in moving
it.The membrane also maintains the cell potential.Proteins embeddedin the cell
membrane can act as molecular signals that allow cells to communicate with each
other.Protein receptors are found ubiquitously and function to receive signals
from both the environment and other cells. These signals are transduced into a
form that the cell can use to directly affect a response. Other proteins on the
surface of the cell membrane serve as "markers" that identify a cell to other cells.
The interaction of these markers with their respective receptors forms the basis of
cell-cell interaction in the immune system.
7-3:Structure.
The cell membrane consists primarily of a thin layer of amphipathic
phospholipids which spontaneously arrange so that the hydrophobic "tail" regions
are shielded from the surrounding polar fluid, causing the more hydrophilic
"head" regions to associate with the cytosolic and extracellular faces of the
resulting bilayer. This forms a continuous, spherical lipid bilayer approximately 7
nm thick, barely discernible with a transmission electron microscope.
The arrangement of hydrophilic and hydrophobic heads of the lipid bilayer
prevent polar solutes (e.g. amino acids, nucleic acids, carbohydrates, proteins,
and ions) from diffusing across the membrane, but generally allows for the
passive diffusion of hydrophobic molecules. This affords the cell the ability to
control the movement of these substances via transmembrane protein complexes
such as pores and gates.
Fig:(18).Diagram of the arrangement of lipid molecules to form a lipid bilayer.
8:The nervous system and the neroun.
The nervous system can be divided into two parts the central nervous
system and the autonomic (automatic) nervous system.The central nervous
system consists of the brain,the spinal ,the peripheral nervos and the nerve fibers
(neurons).The central nervous system controls the transmission of the sensory
information to and from the brain.The autonomic nervous system controls
various internal organs such as the heart,intestine,and glands.
The basic structure unit of the nervous system is the neroun.Basically
aneroun consists of:
1-Cell body:that receives the electrical messages from other neurons
2-Synapses:they are contacts located on the cell body
3-Dendrites:these are parts of the neroun that is specialized in recieiving
information from stimuli or cells
4-Axons(nerve Fibers):that carries electrical signals to muscles,glands,or
other neurons
Fig:(19).Action potentials arriving at the synapses of the upper right neuron
stimulate currents in its dendrites
9:Membrane electrical potentials and nerve impulses
The ability of neurons to receive and transmit electrical signals can be
understood as follows:The walls of the animals cells are thin membranes that
consist of two layers of protein separated by a layer of lipids (fats).Across the
surfaces of the membrane of every neuron is an electrical potential
(voltage)difference due to presence of more negative ions on the inside surface of
the membrane than on th e out side one.The neuron is said to be polarized .The
inside of the cell is typically 60 to 90 mV more negative than the outside .This
potential difference is called 'the resting potential of the neuron'.
The presence of "the resting potential of the neuron" .The presence of " the
resting potential"can be explained by using a model in which a membrane
separates a concentrated neutral solution of KCL from one that is less
concentrated.The KCL in solution forms K+ ions and CL- ions.The membrane
permits the K+ ions to pass through it but does not permit the passage of the CLions .Anet transfer of K+ ions takes place from the high concentration region to
the low concentration region until a condition of equilibrium is attained at which
the resting potential of neuron exists.At normal body temperature the resting
potential "V" is related to the equilibrium concentration ratio c i/c0 across
amembrane through Nernest equation:
V= - 61 log ci/c0
(mV)
Where:
ci is the intracellular ion concentrations
c0 is the extracellular ion concentrations
9-1:The propagation of action potential
When the neuron is stimulated alarge momentary change in th resting
potential occurs at the point of stimulation.This potentail change called "The
action potential".There are negative ions on the outside of the membrane and
positive ions on the inside the neuron is said to be depolarized.Action potential
initiated at 20 mv,action potential lasts up to 30 ms.The action potential
propagates along the axon.The stimulation may be caused by various physical
and chemical stimuli such as heat,cold,light,and sound.
Fig:(20).A:Schematic view of an idealized action potential passes a point on a cell
membrane. B. Actual recordings of action potentials are often distorted compared to the
schematic view because of variations in electrophysiological techniques used to make the
recording.
9-1-1:The nerve conduction
Information is transmitted in human body by electrical pulses in nerve
fibers (axons).The axon has a resting potential of about -80 mV .If the end of the
axon is stimulated the ions pass through the membrane causing it depolarize.The
reversed potential in the stimulated region causes ion movement which in turn
depolarizes the region to the right.Mean while the point of original stimulation
has recovered (depolarized).The action potential lasts from few ms up to 300 ms.
10:The rsistance and capacitanc of membrane.
There are two primary factors can affect the speed of propagation of the
action potential.The first one is the resistance within the core of the membrane
and the second one is the capacitance (or the change stored) across the
membrane.A decrease in either one of them will increase the propagation
velocity.
10-1:The capacitance of Membrane.
The membrane of acell or an axon has a net negative charge on the inner
surface and net positve charge on the outer surface .The charge on the membrane
makes the system acts as a capacitor.In order to get the capacitace of amembrane,
capacitance per unit area Cm is introduced .The cell or axon membrane has a
capacitance per unit area Cm equals 10 mF/m2
10-2:The resistance of an axon.
Since the axon is considered as a cylindrical membrane containing
conducting fluid (axoplasm),the axoplasm resistivity ρo is given by
ρo = R A
L
( Ω .m)
Where:
ρo is the resistivity of the material
L is the length
A is the cross sectional area
11:Direct current circuits:
11-1:Electromotive force (emf)
A source of electromotive force is any device that is able to transform
mechanical, chemical, thermal, or any other non electrical energy into electric
energy or vice versa. This source produces an electric field and thus may cause
charge to move around a circuit.The emf (s) of a source is defined as the work
done per unit charge, so it has unit of J/C or Volt.For the circuit shown in Fig.(5),
if r is the internal resistance of the battery, R is the external resistance and s is the
emf then the current I is given by Ohm’s law as
Fig:(21). Electromotive force.
IR: is the voltage drop across the external resistor
Ir : is the voltage drop across internal resistance r of battery.
11-2:Ohm’s law circuits
Simple circuits that contain resistors in series and in parallel can be
analyzed by using Ohm’s law and the rules for series and parallel
combinations.
11-2-1:For resistors in series
The equivalent resistance R is given by
Fig:(22).Resistors in series
11-2-2:For resistors in parallel
The equivalent resistance is given by
Fig:(23).Resistors in parallel
12:Electric charge and magnetic field.
When an electric charge is at rest, it produces only electric field in the
surrounding space. When the charge is moving it produces both magnetic field
and electric field. Since the electric current is due to moving charges therefore,
associated with any current is a magnetic field. A magnetic field also surrounds
any magnetic substance.In order to describe the field; we must define its
magnitude, or strength, and its direction. The direction of the magnetic field B
at a point is the direction in which the north pole of a compass needle points at
that point.The direction of the magnetic field of a current- carrying wire can be
found using a right-hand rule. Grasp the wire in the right hand, with the thumb
pointing in the direction of the current. The fingers then circle the wire in the
same direction as the magnetic field does
Fig:(24).Electric charge and magnetic field
Because of the magnetic field associated with a moving charge or a current,
there will be an interaction between the moving charge or current and an
external magnetic field. The magnitude of the magnetic field at a point can be
defined in terms of the force acting on a charge moving at this point. Magnetic
force on a charge moving in a magnetic field.When a charge q moves with
velocity v in a uniform magnetic field B, in a direction that makes an angle θ
with the direction of the field, it will be acted by a magnetic force F B so that the
magnitude of the magnetic force is directly proportional to the charge q and the
magnitude of the velocity v of the particle.
Fig:(25).The magnitude and direction of the magnetic force
The magnitude and direction of the magnetic force depends on the
magnitude and direction of the velocity v and on the magnitude and the
direction of the magnetic field B.When the charged particle moves
parallel to the magnetic field vector, the magnetic force on the particle is
zero.When the velocity vector makes an angle θ with the magnetic field,
the magnetic force acts in a direction perpendicular to both v and B.The
magnetic force on a positive charge is opposite to the force on a negative
charge moving in the same direction.The magnetic force is directly
proportional to sin θ. All of these observations can be written as
When the charge q enters the field at angle of 90 (i.e.), perpendicular to
the field, the force is given by
FB = q v
The force FB is in a direction perpendicular to both B and the direction of
motion of q. So it changes the direction of the particle motion, but cannot
change the magnitude of velocity and the kinetic energy of the particle.
When the charged particle moves with constant speed in auniform
magnetic field the magnetic force causes the particle to move in a circular
path
as
in
Fig:(26).Force causes the particle to move in a circular path
fig.(34)
The SI unit of B is the Weber per square meter (Wb/m2) also
called the Tesla (T) this unit can be defined from equation F =
qvB as follows:
Another unit of B is the Gauss (G) it is related to the Tesla by
.
13:The radius of the circular path:
When a particle moves with linear velocity v in a circular
path of radius r it will have a centripetal acceleration ac given by:r
If m is the mass of the particle, then the centripetal force acting on
it is given by
For a particle in a magnetic field the centripetal force is provided
by the magnetic force F c = q v B Therefore; qvB=mv2/r
The unit for m is kg, the unit for v is m/s, the unit for B is Tesla (T), the
unit for the charge (q) is Coulomb (C) and the unit for r is meter. If the
mass and the speed of the charged particle are constants the path. If the
mass and the speed of the charged particle are changing the radiys will
change.If the particle is loosing energy, its speed slows down and the
radiuses of its path will decrease.
Fig:(27). The radius of the circular path
14:The cathode ray oscilloscope (CRO)
The CRO requires a method for deflecting the electron beam in
controlled manner. The electron beam may be focused by one of two
methods, the electrostatic or electromagnetic.
Fig:.(28).The cathode ray oscilloscope (CRO
15:The electrostatic deflection
Electrostatic deflection (or focusing) is caused by an electric field in
the direction of the required deflection. The electric field is generated by
two metal plates whose potential is controlled by the input signal to be
displayed as seen in fig. (38).
If the mass and the speed of the charged particle are changing the
radius will change.
If the particle is loosing energy, its speed slows down and the radius
of its path will decrease.
Fig:(29).The electrostatic deflection
The electromagnetic deflection
The electromagnetic deflection (or focusing) of an electron beam
moving with velocity v is caused by a magnetic field which is
perpendicular to the direction of deflection. The beam will move in a
circular path.Nearly all modem CRO use electrostatic focusing because it is
easier to produce uniform electric fields over large volumes than magnetic
one.
16:Electrical Shocks
It is well known that the current depends on both the voltage of the source and
the resistance of the current path.Electrical resistance within the human body is
relatvely low (about 500 Ω head to foot).The path of least resistance usually follows
the nervous system ,which is agood conductor of electricity,to a certain extent we are
protected by our skin.Electric current produces the physiological effect of electric
shock.A current of 10 mA or more is painful .The danger of electrical shock increases
considerably if the skin is wet at the point of electrical contact.
16-1:Electrical instruments used in medicine.
16-1-1:The electromyogram(EMG).
It is a mean of obtaining diagnostic information about muscles is to measure
their electrical activity.For that purpose, electromyogramdevice is used to record and
study the electrical potential produced by the muscles.
16-1-2:The electrocardiogram (ECG).
It is used to study and record the electrical activity associated with heart.The
used surface electrodes of ECG are located on the left arm (LA),right arm (RA) and
left leg (LL) .Acommon ECG wave from is releated to the heart action.The
electrocariogram voltage signal is typically about 1 mV and the amplitude can reach 5
mV
16-1-3:The electrooculogram (EOG).
It is used to record the potential changes produced by the eye when the retina is
exposed to a flash of light.The electrooculogram(EOG) is the recording of potential
changes due to the eye movement.It provides information on the orientation of the eye
and its angular velocity.
Solution of some selected problems
Example (1):
A charge of 2μC experiences a force of 34 N when placed at a point in an
electric field.Calculate the electric field strength at the point?
Q = 2μC= 2x 10-6 C
F = 34 N
E=F/Q
(N/C)
E=34 N /2x 10-6 C = 68x 10-6 (N/C)
Example (2):
The work done in bringing a charge of 4 C from one point to another is 10
J .What is the potential difference between the two points?
Q=4C
W = 10 J
V = W = 10 = 2.5 V
Q
4
Example(3):
The potential difference between two points is 12 V.Find the work done to
move a charge of 8 C between the two points?
V = 12 C
Q=8C
W=QV = 8x12 = 96 (J)
Example(4):
If the potential difference between two parallel plates separated by a
distance 1 mm is 400 v,Find the electric field intensity between the two plates.?
ΔX = 1mm = 1 x 10-3 m
ΔV = 400
(V/m)
E = ΔV = 400 = 4 x 105
ΔX
1 x 10-3
(V/m)
Example (5):
If the thickness of a membrane is 80 x 10-10 m and the potential differences
between its two surfaces is 80 mV, find the electric field intensity within the
membrane?
ΔX = 80 x 10-10 m
ΔV = 80 mV = 80 x 10-3 (V)
E= ΔV = 80 x 10-10 = 107
ΔX
80 x 10-3
(V/m)
Example (6):
The effective area of the plates of a parallel plate capacitor is 20 cm 2 .The
distance between the plates is 1mm .Given that ε0 = 8.85 x 10-12 F cm-1 ,find the
capacitance.
A=20 cm2 = 20 x 10-4 m2
d = 1 mm= 1 x 10-3 m
C = ε0 A = 8.85 x 10-12 x20 x 10-4 = 1.78 x 10-11 F = 17.8 pF
d
1 x 10-3
Example: (7).
A capacitor of capacitance 0.47 μF carries a charge of 2μC.
Calculate :(i) The potential difference between the plates
(ii)The energy stored
C = 0.47 μF = 0.47 x 10-6 F
Q = 2 x 10-6 C
(i) C = Q
V
V = Q = 2 x 10-6 C = 4.26 V
C
0.47 x 10-6 F
(ii): W= 1 CV2 = 1 (0.47 x 10-6 ) (4.26)2 = 4.26 x 10-6 (J)
2
2
Example (8):
If the effective area of a parallel plate capacitor is 20 cm2 and the distance
between its plates is 1 mm, find its capacitance when:
(i): The gap between its plates is filled with air.
(ii): The gap between its plates is filled with mica (K =7)
A=20 cm2 = 20 x 10-4 m2
d = 1 mm= 1 x 10-3 m
C = ε0 A = 8.9 x 10-12 x 20 x 10-4 = 1.78 x 10-11 F = 17.8 pF
d
1 x 10-3
(ii): C = KC0 = 7 x 0.178 = 1.2 x10-10 F
Example(9):
A current of 4 mA flows through a bulb.How much charge enters the bulb
in
1-One second
2-One minute
3-One hour.
1- Q = I t =(4x10-3) (1) = 4x10-3C
2- Q = I t =(4x10-3) (1x60) = 2.0x10-1C
3- Q = I t =(4x10-3) (1x60x60) = 20.0x10-1C
Example(10):
If the charge of one electron is 1.6x10
-19
C,how many electrons flow past
any point in a circuit for which 20 A current flows for 6 sec?
Q = I t =(20x6) = 120 C
Q =ne
n = Q / e (120/1.6x10 -19) = 7.5x 10 20
Example(11):
If aconductor of length 20 m end cross-sectional area 1mm carries an
electric current 20 mA,
Find:
1- Its resistance if you know that its resistivity is 5x10 -6 (Ω m )
2-Its conductivity
3-The potential difference across the conductor
1-R = ρ
L
A
= 5x 10 -6 (Ω m ) x
20 =50(Ω )
2x 10 -6
2- σ = 1 / ρ = 1/ 5x 10 -6 = 0.2x 10 6(Ω -1 m-1)
3- V = I R = (20x 10 -3 ) (50) = 0.1 V
Example(12):
An electric motor operating at 220 V draws a current of 4 A.
Calculate:the power of the motor
P = IV = 4X220 = 880 (W)
Example (13):
Acharge of 2µC experiences a force of 34 N when placed at a point in an
electric field.calculate the electric field strength at the point?
F=34 N
q = 2µC
E=F/q
E =
34 = 1.7x107 ( N/C)
2x10-6
Example (14):
Calcullate the magnitude of the force on charge of 6 µC when placed in an
electric field of strength 4 x10-3 NC-1?
E=F/q
F= Eq
F = (4x10-3) (5x10-6) = 2x10-8 N
Example(15):
A biological membrane has an area 10-6 cm2 and thickness 80 x 10-10
m2.If the dielectric of this membrane is 5 ,calculate its capacitance.Then
find the energy stored in this membrane if the voltage across it is 65 mV .
( ε0 = 8.9 x 10-12 F/m)
A=10-6 cm2 = 10-6 x 10-4 m2
d = 80 x 10-10 m
K=5
V = 65 mV = 65x10-3
C = ε0 A = ε0 K A (8.9 x 10-12 ) x5 x 10-6 x 10-4 = 1.78 x 10-11 F = 17.8 pF
d
d
80 x 10-10
C = 5.56 x10-13 F
C = 0.556 pF
W=1/2 CV2 = 1/2 (5.56 x10-13 )( 65x10-3) 2 = 1.175 x10-15 (J)
Example (16):
Calculate the capacitance of a membrane whose area is 5 x 10-2 cm2 if you
know that Cm = 10 mF/m2
Cm = 10 mF/m2 = 10 x10-3 F/m2 = x10-2 F/m2
A = 5 x 10-2 cm2 = 5 x 10-2 x10-4 m2 = 5 x10-6 m2
C = Cm A = x10-2 x 5 x10-6 = 5 x10-8 (F)
Story Problems
1-A current of 5 mA flows through a bulb.How much charge enters the bulb in
1-One second
2-One minute
3-One hour.
2-If the charge of one electron is 1.6x10 -19 C,how many electrons flow past any
point in a circuit for which 20 A current flows for 5 sec?
3-If aconductor of length 20 m end cross-sectional area 2mm carries an electric
current 20 mA,
Find:
1- Its resistance if you know that its resistivity is 5x10 -6 (Ω m )
2-Its conductivity
3-The potential difference across the conductor
4-An electric motor operating at 110 V draws a current of 2 A.
Calculate:the power of the motor
5-Acharge of 2µC experiences a force of 30 N when placed at a point in an
electric field.calculate the electric field strength at the point?
6-Calcullate the magnitude of the force on charge of 5 µC when placed in an
electric field of strength 4 x10-3 NC-1?
7-An electric heater can draw a current of 0.5 amperes when connected to a
source of 120 V. What is its resistance?
8-Calculate the resistance of a gold rod that is 10 cm long and cross-sectional
area of 2.0 xl0-4 m2. (p =2.44 xl0-8).
9-How many electrons pass through a wire when a current of 0.5 A passes for
5seconds.
10-An electron gun in a CRO shoots out a beam of electrons. The beam
current is IJIA. How many electrons per second strike the screen of the CRO?
How much charge strikes the screen per minute?
11-What is the current in a bulb of 10 Q resistor when it is operating on 220
V?
12-Determine the potential difference between the ends of a wire of 5H
resistance when a charge of 720 C passes through it per minute.
13-A copper bar carrying a current of 1200 A has a potential drop of 1.2 mV
along 24 cm of length. What is the resistance per meter of the bar?
14-Calculate the internal resistance of an e.m.f source which has an emf of 220
volt and a terminal yoltage (across the external resistor) of 200 V when
supplying a current of 40 A.
15-A heater is labeled 1600W/220V. How much current does the heater draw
from a 220 V supply?
16-A tank containing 200 liters of water was used as a constant • temperature
bath. How long would it take to heat the bath from 20°C to 25°C with a 250 W
heater?
17- What is the resistance of a 200 m long wire of silver, which has a crosssectional area of 0.33 mm , and resistivity of 1.6 xlO-8 Sm.?
18-A coil of wire has a resistance of 25 £1 at 20°C and aresistance of 25.17 Q at
35°C. What is its temperature coefficient of resistivity?
19-A strain gauge of length 1.8-cm is used for the measurement of the force of
the cardiac muscle. If the gauge factor is 2.5 and the bridge constant is 0.7
mA. what is the muscular displacement that causes a current of 9mA to pass
through the galvanometer?
References
a. Adair, R.K.(1992):"Criticism of Lendev's Mechanism for the Influence of
Weak Magnetic Fields on Biological System "Bioenergetics 13:231-235.
b. Cantor and P. Schimmel (1985). Biophysical Chemistry, Vol. I, II and III.
C.R.
c. Fadel M. Ali :(2003):Principles Biophysics book
d. Hoppe, W. Lohman, H. Markl and H Ziegler (1983). Biophysics. New
York,pp101-120
e. Ireifelder W.H. Freeman (1982):Physical Biochemistry. EMF Health
Report 2
f. Gckerman, L.B.M. Ellis and L.E. Williams (1979):Biophysical Science..
Prentice-Hall Inc., New
g. Good man ,R.and Henderson A.S(1990):Exposures of cells to extremely low
frequency eletromagnetic fields:Regulatioship to malignancy?Cancer Cells
2;355-359.
h. Lendev ,V.V(1991):Possible Mechanism for WeakMagnetic Fields on
Biosystem "Bioelectromagnetics"N.Y.12:71-75.
i. Liboff,A.R.;Smith,S.D and McLeod,B.R (1987). Expermintal Evidence for
Ion –cyclotorn Responance Mediation of Membrane Transport.In
Mechanistic Approaches to Interactions of bioelectricity .New York.pp210215.
j. M.Roushdy (2007):Electricity and Waves Book.
k. Physics for Scientists and Engineers, Serway & Beichner. Fifth edition.
l. Fundamentals of College Physics. Peter J. Nolan. Second edition. WCB
Publishers.
m. College Physics. Vincent P. Coletth. Mosby Publishers.
n. Physics. Serway & Faughn .Holt, Rinehart, Winston Publishers.
BioPhysics & Physics Resources on the Web
a. http://www.geocities.com/awadkt/
b. http://www.brainpop.com/science/
c. http://www.kathimitchell.com/elect.htm
d. http://www.kathimitchell.com/magnet.htm
e. http://host.exploreleaming.com/ESClassic/index
f. http://antoine.frostburg.edu/chem/senese/101/index
g. http://www.ahpcc.unm.ed
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