Download 2. Laws of thermodynamics

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Unit 9: Fluid Mechanics and Thermodynamics – Thermodynamics
OBJECTIVES:1
II. FLUID MECHANICS AND THERMAL PHYSICS
B. Temperature and Heat
1. Mechanical equivalent of heat: Students should understand the “mechanical equivalent of
heat” so they can determine how much heat can be produced by the performance of a specified
quantity of mechanical work.
2. Heat transfer and thermal expansion: Students should understand heat transfer and thermal
expansion so they can:
a. Calculate how the flow of heat through a slab of material is affected by changes in the
thickness or area of the slab, or the temperature difference between the two faces of the
slab.
b. Analyze what happens to the size and shape of an object when it is heated.
c. Analyze qualitatively the effects of conduction, radiation, and convection in thermal
processes.
C. Kinetic theory and thermodynamics
1. Ideal gases
a. Students should understand the kinetic theory model of an ideal gas so they can:
1.) State the assumptions of the model.
2.) State the connection between temperature and mean translational kinetic energy
and apply it to determine the mean speed of gas molecules as a function of their mass
and the temperature of the gas.
3.) State the relationship among Avogadro’s number, Boltzmann’s constant, and the gas
constant R and express the energy of a mole of a monatomic ideal gas as a function of
temperature.
4.) Explain qualitatively how the model explains the pressure of a gas in terms of
collisions with the container walls and explain how the model predicts that, for fixed
volume, pressure must be proportional to temperature.
b. Students should know how to apply the ideal gas law and thermodynamic principles so
they can:
1.) Relate the pressure and volume of a gas during an isothermal expansion or
compressions.
2.) Relate the pressure and temperature of a gas during constant-volume heating or
cooling, or the volume and temperature of a gas during constant-pressure heating or
cooling.
3.) Calculate the work performed on or by a gas during an expansion or compression at
constant pressure.
1
These are the outlined objectives of the AP Physics B course as laid out by the College Board. We will continue to
build this outline throughout the year. We do not do all of the objectives listed in the AP outline, as some are only
for AP Physics C. Therefore missing numbers or letters is intentional.
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
4.) Understand the process of adiabatic expansion or compression of a gas.
5.) Identify or sketch on a PV diagram the curves that represent each of the above
processes.
2. Laws of thermodynamics
a. Students should know how to apply the first law of thermodynamics so they can:
1.) Relate the heat absorbed by a gas, the work performed by the gas, and the internal
energy change of the gas for any of the processes above.
2.) Relate the work performed by a gas in a cyclic process to the area enclosed by a
curve on a PV diagram.
b. Students should understand the second law of thermodynamic, the concept of entropy,
and heat engines and the Carnot cycle so they can:
1.) Determine whether entropy will increase, decrease, or remain the same during a
particular situation.
2.) Compute the maximum possible efficiency of a heat engine operating between two
given temperatures.
3.) Compute the actual efficiency of a heat engine.
4.) Relate the heats exchanged at each thermal reservoir in a Carnot cycle to the
temperatures of the reservoirs.
NOTES:
I. Temperature and Heat
A. Mechanical equivalent of heat
1. Heat and temperature are ___________________.
a. Internal energy/thermal energy: the ____________________________ inside of an object
due to the __________________ of the atoms and molecules
1.) Symbol:
2.) SI unit:
b. Temperature: A _________________ connotating the ____________________________
___________________________________; relative to another object, something can be
_____________________ where the hotter object can transfer energy to the colder object;
measurable by many scales
1.) Symbol:
2.) SI unit:
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
Conversion to
Conversion
Conversion to
Fahrenheit
to Celsius
Kelvin
Convert to C then
F
x
C
x
K

to K
Convert to C then to F
x
Put 273.15 into calculator memory.
c. Heat: Energy as it ___________ from a higher-temperature object to a lower-temperature
object ____________________________________; ___________________
1.) Symbol:
2.) SI unit of heat:
3.) Traditional unit of heat: kcal where 1.0 kcal of heat transferred into water raises the
temperature of 1kg of water 1⁰C
2. _____________________________: __________ of ________ can transfer ______ of
_______. (Put in calculator memory.)
3. Example 1: When a 3.0g bullet, traveling with a speed of 400m/s, passes through a tree its
speed is reduced to 200m/s. How much heat is produced and shared by the bullet and the tree?
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
B. Heat transfer and thermal expansion
1. Most substances __________________ and ____________________.
2. ____________________________: The ________________ any ____________________
(length, width, or height) of a solid __________________________
a. Formula:

_____ is the __________________________

_____ is the _________________________________
o
Each substance has a unique coefficient.
o
Units: ⁰C-1 or, less commonly, K-1 if temperature is measured in K in that
problem

_____ is the initial length (change in length is proportional to original length
because a longer object has more substance to expand.)

_____ is the temperature change
b. Examples:
1.) Conceptual example: The coefficient for glass is almost 3x bigger than for Pyrex.
Pouring boiling water into a cool glass cup expands the interior surface 3x more than it
would a Pyrex cup…glass is not as heat safe.
2.) Conceptual example: Bimetalic strip in a thermostat…room air heats up > strip bends
outward, tipping mercury over the two wires to begin electric current flow to furnace
3.) Example 2: When engineering, we need to allow for expansion by leaving gaps. Steel
railroad tracks are laid a day when the temperature is 5⁰C. What size expansion gaps are
needed between 12m long rail sections if the temperature range in that region is -10⁰C
to 55⁰C? The coefficient of expansion for steel is 12E-6⁰C-1.
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
3. Volume expansion
a. Formula:

_____ is the _________________________________ in ⁰C-1 (or K-1)
o
𝛽 = 3𝛼 (not 𝛼 3 …units wouldn’t work, and can be found algebraically.)
o
𝑆𝑒𝑒 𝑝𝑎𝑔𝑒 365 𝑓𝑜𝑟 𝑒𝑥𝑎𝑚𝑝𝑙𝑒𝑠 𝑜𝑓 𝛼 𝑎𝑛𝑑 𝛽.
b. Examples
1.) Example 3: The 70-L steel gas tank of a car is filled to the top with gasoline at 20⁰C.
The car is then left to sit in the sun, and the tank reaches a temperature of 40⁰C. How
much gasoline do you expect to overflow from the tank? The coefficients of volume
expansion for gasoline and steel are, respectively, 950E-6 ⁰C-1 and 36E-6⁰C-1.
2.) Conceptual example: A slab of metal with a hole cut in it is heated. Does the hole
expand or contract?
3.) Conceptual example: When a metal jar lid is stuck on a glass jar, how could you use
thermal expansion to loosen the lid?
4.) Conceptual example: Why is a blow torch standard equipment for a plumber?
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4. Heat transfer: There are three ways heat transfers from one object to another.
a. _____________________:
1.) Heat transfer by the ________________________ within a fluid over relatively large
distances
2.) Examples:
a.) Forced convection: Furnaces blowing hot air through air ducts
b.) Natural examples: hot air rising, Gulf stream, weather, boiling water
b. _____________________:
1.) Heat transfer ________________________ with a _________________________
from one end to the other; molecules at the hot end vibrate more readily, ___________
with molecules at the cooler end and transferring energy to them.
2.) Conductivity _________________ ____________ and ________.
a.) Formula:
o
𝐻 is the _____________________
o
𝑘 is the _________________________ of the material in 𝑠∙𝑚∙℃
o
A is the _________________________
o
∆𝑇 is the _____________________________ on each side
o
𝑙 is the thickness (__________________________)
𝐽
b.) Units:
3.) Example 4: A major source of heat loss from a house is through the windows.
Calculate the rate of heat flow through a glass window 2.0m x 1.5m in area and 3.2mm
thick if the temperatures at the inner and outer surfaces are 15.0⁰C and 14.0⁰C
respectively. The thermal conductivity of glass is 2.0E-4
𝑘𝑐𝑎𝑙
𝐽
or 0.84
𝑠∙𝑚∙℃
𝑠∙𝑚∙℃
.
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
c. _____________________:
1.) Heat transfer ___________________________ by means of ___________________
______________________________
2.) Radiation depends on ___________________ (ability to emit/absorb
electromagnetic radiation) and ___________.
a.) Objects emit and absorb radiation ___________________, and the net in/out
ratio determines whether the object heats up or cools off.
b.) Dark objects have high emissivity…a ________________ is an object that absorbs
all the electromagnetic radiation falling on it.
II. Kinetic Theory
A. ________________________________
1. Characteristics:
a. There are a very ____________________________ that move in _____________
directions with a _________________________ in straight lines until they collide with each
other or the container walls.
b. The average separation of molecules is much greater than the size of each molecule.
c. The molecules obey the laws of classical mechanics, and they interact only when they
collide. (There are no attractive forces between the molecules.)
d. Faking it to be ideal: All _____________________________ and therefore do not transfer
momentum to container walls.
e. All molecules are alike (pure substance).
2. ______________________________
a. Relates pressure, Kelvin temperature, volume, and number of moles of gas
b. Formula:
1.) P is ____________ in Pa
2.) V is ____________ in m3
3.) n is the number of ____________ present
4.) N is the number of ____________ = n x 6.022E23 molecules/mol (Avogadro’s # is N0)
5.) R is the ____________________=8_________ (Different from chemistry due to units)
6.) 𝑘𝐵 is ________________________= R/N0 = ____________
7.) T is ____________ in Kelvin
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
3. Work done by a gas during expansion/compression at a constant pressure2:
4. Examples:
a. Example 5: An ideal gas initially at 20⁰C under 1 atm of pressure has a volume of
3L in a container with a piston on top. The piston is pushed downward, compressing the
gas to a volume of 1L as the temperature rises to 40⁰C. What is the pressure of the gas
when the piston is compressed? If the piston has a surface area of 0.02m2 and has a
negligible mass, how much force is required to hold the piston in place?
b. Example 6: A tire is filled to a gauge pressure of 300kPa at 5⁰C. The temperature
goes up to 40⁰C. What fraction of the air must be let out to reduce the pressure back to
the original level?
2
In AP Physics B, W is defined as “work done ON a system” and is (+). That makes sense since work is literally “added” to the
system. Therefore when work is done BY a system (like an expanding gas moving the walls of its container), then W should bear
a (−) sign. In the case of an expanding gas the “work” term is simply PΔV, so it bears a (−) sign. THIS IS DIFFERENT FROM YOUR
BOOK’S CONVENTIONS.
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
B. Kinetic theory of an ideal gas
1. Assumptions of this theory: See the properties of an ideal gas, II. A. 1.
2. The ______________________________ in an __________ follows this formula:
a. 𝑣 𝑟𝑚𝑠 is the square root of the mean velocity3 of all the particles (“root mean squared”)
3
2
1
2
b. The is really in three dimensions, because the particles move randomly in any of the 3
dimensions.
3. The ____________________________ can be found by:
a. 𝑀 is the ______________ in kg/mol4
b. 𝜇 is the _____________________
4. Examples:
a. Example 7: 0.2 mol of oxygen at 300kPa take up a volume of 0.005L. What is the average
translational kinetic energy per molecule? What is the total translational kinetic energy of
the gas?
b. Example 8: Find the 𝑣𝑟𝑚𝑠 of 2.5 mol of hydrogen gas at 4atm and 300K. The molar mass of
(diatomic) hydrogen gas is 2g/mol.
3
translational (straight-line) velocity, not rotational or vibrational…This course looks only at translational velocity
when examining kinetic theory of gasses.
4
Easy molar mass calculator: http://www.lenntech.com/calculators/molecular/molecular-weight-calculator.htm
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
c. Conceptual example: Explain qualitatively how the model explains the pressure of a gas in
terms of collisions with the container walls and explain how the model predicts that, for fixed
volume, pressure must be proportional to temperature.
III. Laws of Thermodynamics
A. Zeroth Law of Thermodynamics: If system A & system B are in thermal equilibrium with system C,
A and B are also in thermal equilibrium with each other.
1. Uniform temperature is the indicator of thermal equilibrium.
2. There is no net heat flow in a system in thermal equilibrium.
3. Example: The two containers in (a) with adiabatic (insulating)
walls have the same temperature. When connected by a
diathermal wall (heat conducting), heat does not flow.
B. First Law of Thermodynamics: The internal energy of a system may
be increased or decreased by gaining or losing heat energy. If energy
is added to the system in the form of heat, the internal energy
increases, according to the formula:

𝑄 is the __________________ into the system

𝑊 is the work done _______ the system _______ the environment.
o
Compression is _______. (System does –W on environment.)
o
Expansion is _______. (System does +W on environment.)
1. Example 9: 500 J of heat is added to system while the system does 200 J of work on the
environment. What is the system’s change in internal energy?
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
C. PV diagrams: a tool to analyze thermodynamic relationships
1. These show pressure v. volume for a closed system (constant 𝑛).
2. With 𝑛 and 𝑅 constant, T 𝛼 PV, so we get:
lower
T
higher
T
3. Area under the curve & work done ON the gas BY the environment above the gas. (Work is
always considered done on an object.:
W = Fd
W = (PA)d
W = P(Ad)
W = PΔV
(If volume increases, W is negative because the gas did work on
the environment, and F and d are in opposite directions,
so we add the negative sign to the equation.)5
___________ is the +/- of the ______________________ of a ___________.
5
In AP Physics B, W is defined as “work done ON a system” and is (+). That makes sense since work is literally “added” to the
system. Therefore when work is done BY a system (like an expanding gas moving the walls of its container), then W should bear
a (−) sign. In the case of an expanding gas the “work” term is simply PΔV, so it bears a (−) sign. THIS IS DIFFERENT FROM YOUR
BOOK’S CONVENTIONS.
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
4. PV diagram for an ______________________: ___________________, changing volume due
to change in temperature and work done
a. Conceptual example: A container with a piston on top is heated (ΔT), pushing the piston
upward (-W on gas) to maintain constant pressure within the container. (In this
case, Pgas = Patm).
b. Example 10: (a) Sketch a PV diagram when a gas is slowly compressed at a constant
pressure of 2.0atm from 3.0L to 1.0L. In this process, some heat flows out, and the
temperature drops. (b) If the gas loses 1400J of heat in the process, find the heat added to
the gas, (c) the work done on the gas, and (d) the change in internal energy. (e) Does the
temperature increase or decrease?
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
5. PV diagram for an ___________ (______________)___________: ________________,
changing pressure due to change in temperature
a. Example 11: Sketch a PV diagram and calculate the work done when a gas is heated, but
the volume is held constant.
b. Lessons learned:

Work done in an isochoric process is zero because there is no displacement of the
gas if the volume doesn’t change. W = 0

However, U does increase because heat (Q) was added.
6. PV diagram for an ______________________: ___________________,, changing pressure
and volume
a. ____________________: Something that maintains a constant temperature, such as by
being very large or very insulating6; putting the container in contact with a heat reservoir
causes it to maintain its temperature.
1
b. 𝑃𝛼 𝑉 because in 𝑃𝑉 = 𝑛𝑅𝑇, 𝑛𝑅𝑇 are constant in an isothermal process and…
6
Lake Erie is a great heat reservoir, which is why it stays warm when winter comes, causing lake effect snow.
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
c. Example 12: For an isothermal compression, sketch a PV diagram starting from P = 4 Pa
and V = 1m3. Find the change in K and U. Is the work positive or negative?

Important:

Therefore
o

(True for isothermal expansion as well.)
The curved line is called an ______________.
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
7. PV diagram for an ___________________________
a. ______________________________ with the environment in an adiabatic process so that
b. Done by either…
1.) Putting the gas in a very ______________________________, or…
2.) Making the change very _____________ so that there is not enough time for heat
exchange.
c. Work is still done, so
therefore ___ changes, and therefore ___ changes…as ___ changed..
d. ____________________________:
1.) Characteristics:

______________________ because

______________________ so

______________________ so

______________________.
2.) On the left side of the graph below, the ending point is below the isotherm (right.)
e. ____________________________:
1.) Characteristics:

______________________ because

______________________ so

______________________ so

______________________.
2.) On the right side of the graph above, the ending point on the left is above the
isotherm.
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
8. Make a graphic organizer for PV diagrams:
D. Second Law of Thermodynamics
1. The 2nd Law states that _________________________________________________________
____________________________________________________________________________.
a.  there can be ______________________________________, that is, one that can
change a given amount of heat completely into work.
b.  natural processes tend toward a state of ____________________ (_________).
c.  a perpetual motion machine is impossible.
2. ________________________: A device that _______________________ to ____________
or _______________ energy by ___________________ along a ________________________.
a. Example: Burn coal to turn water to steam, which causes a turbine to turn, creating
electrical energy.
b. Characteristics: the engine carries a substance through a _________ in which…
1.) heat is absorbed from a source at a higher T
2.) work is done by the engine (flowing out to
the right)
3.) heat is expelled by the engine to a reservoir
at a lower temperature (heat sink, bottom.) This
heat is wasted (entropy).
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
c. ________________________
1.) the ratio of work done |𝑊|to input heat |𝑄𝐻 |
of a heat engine by the formula
2.) What is lost ______________________.
d. ___________________________ (ideal engines)
1.) A theoretical engine with ____________________ because the engine operates in a
___________________ in which both system and environment return to their intial
states.
a.) No increase in entropy
b.) For any _____________________, the Carnot engine represents the maximum
efficiency of any engine for a set temperature range with zero increase in entropy.
2.) __________________________:

Isothermal expansion with
temperature 𝑇𝐻 where the gas
expands, absorbing heat 𝑄𝐻

Adiabatic expansion where
the gas expands without absorbing
heat. This lowers the temperature to 𝑇𝐶 .

Isothermal compression at 𝑇𝐶 with constant temperature so that heat flows out.

Adiabatic compression replenishes the temperature to 𝑇𝐻 .

The area inside of the curve equals the work, and, to keep the energy
conserved:
where 𝑄𝐶 is the heat flow to the output reservoir
Therefore 𝑊 = 𝑄𝐻 − 𝑄𝐶
giving us
𝑒=
|𝑄𝐻 − 𝑄𝐶 |
|𝑄𝐻 |
which gives us
This is the efficiency equation for a Carnot engine.
GUIDED NOTES, a.k.a. How much stuff is in this unit!?!?
e. Example 13: An automobile engine produces 9.2E4 J of heat while it does 2.3E4 J of
mechanical work. What’s its efficiency?
f. Example 14: An engine manufacturer makes the following claims: The heat input per
second of the engine is 9.0kJ at 375K. The heat output per second is 4.0kJ at 225K. Do you
believe the claims?
E. Third Law of Thermodynamics: It is impossible to lower the temperature of a system to absolute
zero.