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ISNS 3371 - Phenomena of Nature
Phase Change Diagram
ISNS 3371 - Phenomena of Nature
Specific Heat Capacity, c: Thermal inertia
Specific Heat Capacity is the quantity of heat required to change the
temperature of 1 gram of a substance by 1° C.
Q units of of thermal energy added to 1 gram of a substance produces a
temperature change of ∆T,
Q = c x ∆T
Specific heat , c, of a substance is the heat capacity per unit mass.
For m grams of a substance,
Q = cm ∆T or ∆T = Q/cm
Water has high specific heat capacity - used as a cooling fluid.
Specific heat capacity of water is 1 calorie/gram-deg. C
ISNS 3371 - Phenomena of Nature
Heat of Fusion Measurement
Add 10 grams of ice (at 0º C) to 100 grams of water.
What is the heat of fusion of water?
Mass of water=M
Mass of ice =m
Hf= heat of fusion of water
To = initial temperature of ice
Tw = initial temperature of water
Tf = final temperature of water
Heat required to melt the ice = mHf
Heat required to raise the temperature of melted ice to final
temperature of water = cm ∆T = cm(Tf - To)
Heat absorbed from water = cM ∆T = cM(Tw-Tf)
ISNS 3371 - Phenomena of Nature
Heat of Fusion
Heat Absorbed by Ice
Heat Transferred from Water
Q1 = cm(Tf - To) +mHf
Q2 = cM(Tw - Tf)
Equate heat absorbed by ice to heat transferred from water
cm(Tf - To) + mHf = cM(Tw - Tf)
To = 0 and c = 1, so
mHf = M(Tw - Tf) - m Tf
Hf = M/m((Tw - Tf) - Tf
ISNS 3371 - Phenomena of Nature
Heat of Fusion
Heat Absorbed by Ice
Heat Transferred from Water
Q1 = cm(Tf - To) +mHf
Q2 = cM(Tw - Tf)
Equate heat absorbed by ice to heat transferred from water
cm(Tf - To) + mHf = cM(Tw - Tf)
To = 0 and c = 1, so
mHf = M(Tw - Tf) - m Tf
Hf = M/m((Tw - Tf) - Tf
Hf = 80 cal/gr
ISNS 3371 - Phenomena of Nature
Change of State (Phase Change)
Example:
Add 10 grams of ice at 0º C to 100 grams of water at 30 º C.
What is the final temperature of the water?
Heat Absorbed by Ice
Heat Transferred from Water
Mass of ice =m
Mass of water=M
Hf= heat of fusion of water: 80 calories/gram
To = initial temperature of ice
Tw = initial temperature of water
Tf = final temperature of water
Q=cm(Tf - To) +mHf
Q=cM(Tw-Tf)
ISNS 3371 - Phenomena of Nature
Change of State (Phase Change)
Heat Absorbed by Ice
Heat Transferred from Water
Mass of ice = m = 10 grams
Mass of water = M = 100 grams
Hf= heat of fusion of water:
80 calories/gram
Q = cm(Tf - To) +mHf
Q = cM(Tw - Tf)
Q = 1 x 10(Tf - 0) + 10 x 80
Q = 1 x 100(30 - Tf)
Equate heat absorbed by ice to heat transferred from water
10Tf + 800 = 3000 - 100Tf
110Tf = 3000 - 800
Tf = 2200/110
ISNS 3371 - Phenomena of Nature
Change of State (Phase Change)
Heat Absorbed by Ice
Heat Transferred from Water
Mass of ice = m = 10 grams
Mass of water = M = 100 grams
Hf= heat of fusion of water:
80 calories/gram
Q = cm(Tf - To) +mHf
Q = cM(Tw - Tf)
Q = 1 x 10(Tf - 0) + 10 x 80
Q = 1 x 100(30 - Tf)
Equate heat absorbed by ice to heat transferred from water
10Tf + 800 = 3000 - 100Tf
110Tf = 3000 - 800
Tf = 2200/110
Tf = 20º C
ISNS 3371 - Phenomena of Nature
Vapor Pressure and Boiling Point
Evaporation in a closed container will proceed until there are as many
molecules returning to the liquid from the vapor above the liquid as there
are escaping - the vapor is then said to be saturated. The pressure of that
vapor is called the saturated vapor pressure.
Molecular kinetic energy is greater
at higher temperature - more
molecules can escape the surface
and the saturated vapor pressure is
correspondingly higher. If the liquid
is open to the air, then the pressure
of the air opposes the escape of
the molecules. The temperature at
which the vapor pressure is equal
to the atmospheric pressure is
called the boiling point.
ISNS 3371 - Phenomena of Nature
Evaporation vs Boiling
Both start with a liquid and end with a gas. But they are different processes.
Evaporation:
Strictly a surface phenomena
Occurs at any temperature
Some hotter (faster)-than-average particles overcome the forces
they feel from their neighbors and escape the liquid, taking
their heat energy with them.
Forces only felt from particles beneath them
Boiling:
Happens throughout the liquid
Occurs at the boiling point/temperature
Average motion of particles is fast enough to overcome the forces
holding them close together - all the particles are trying to escape liquid turns to vapor
Forces felt from particles all around them
Boiling point dependent on atmospheric pressure - steam bubbles form
in liquid only when vapor (steam) pressure exceeds atmospheric
pressure (plus pressure of water pushing down)
ISNS 3371 - Phenomena of Nature
The Boiling Point Depends on the Liquid Temperature and
the Atmospheric Pressure
Boiling (evaporation) cools the liquid
- when 100º C water is boiling, it is in thermal equilibrium
- it is being cooled by the boiling as fast as it is being heated by the
heat source - if not the water temperature would continue to rise
ISNS 3371 - Phenomena of Nature
Pascal's Law
1) The pressure is the same all over the bottom of a rectangular
tank of liquid. More generally, the pressure is the same at all
points which are at the same level in one liquid (or gas).
Remember:
Pressure is created by atomic and molecular collisions
Pressure = force per unit area
Force has direction. Force giving rise to pressure is
always perpendicular to the surface.
2) Fluid pressure on any surface is perpendicular to it. (A diver
carrying a coin finds the pressure perpendicular to its surface
whatever direction it faces.)
3) At any place in a fluid, pressure pushes equally in all directions.
(A diver carrying a coin finds the same pressure on the coin
whatever direction it faces.)
ISNS 3371 - Phenomena of Nature
Pascal's Law, cont.
4) Pressure is transmitted without loss from one place to
another throughout a fluid. (push a piston in at one place in a
hydraulic system and the pressure you exert is carried to
every wall and any other pistons in the system.)
5) The difference in pressure between any two places in a
single fluid is given by h x d where h is the vertical difference
of level and d is the density of fluid.
ISNS 3371 - Phenomena of Nature
The Gas Laws
ISNS 3371 - Phenomena of Nature
The Gas Laws
ISNS 3371 - Phenomena of Nature
Properties of gases
•
•
•
•
•
•
Very compressible.
Acquires shape of its container,
Completely fills any closed container.
Very low density compared with a liquid or a solid.
Exhibits a pressure on the walls of its container.
Pressure = force per unit area
P = F/A
Force has direction. Force giving rise to pressure is
always perpendicular to the surface.
ISNS 3371 - Phenomena of Nature
Gas Laws
P = pressure of gas
V = volume of gas
T = absolute (kelvin) temperature of gas
– Boyle's Law:
– Charles’ Law:
– Guy Lussac’s law
– General or ideal gas law
PV = constant, if T is constant
V/T= constant, if P is constant
P/T = constant, if V is constant
PV/T = constant
PV = n RT
• R = general gas constant = 8.314 joules/degree-mole
• n = number of moles of gas - a mole is 22.4 liters of a gas
Ideal gas - one in which we can ignore interactions between the gas
molecules. Most gases behave in the same universal way as long as the
temperature is kept far from the liquefaction temperature.
ISNS 3371 - Phenomena of Nature
Guy Lussac’s Law and Absolute Zero
Remember third law of thermodynamics:
No system can reach absolute zero.
How do you determine absolute zero?
Consider Guy Lussac’s law:
P/T = constant, if V is constant
This is for an ideal gas
Temperature must get smaller as pressure gets smaller
Theoretically, as pressure goes to zero, temperature must go
to some smallest value
This value is absolute zero and can be determined by
measuring the pressure and temperature of a gas at several
values and extrapolating to zero pressure
ISNS 3371 - Phenomena of Nature
Boyle’s Law
Boyle’s Law animation
PV = constant, if T is constant
ISNS 3371 - Phenomena of Nature
The Law of Adiabatic Expansion (or Compression))
Any gas will cool that is allowed to expand freely from a higher pressure to a
lower pressure without the transfer of external energy to the gas. Similarly,
a gas will heat if compressed from a lower to a higher pressure in the
absence of a transfer of energy from the gas.
Consider gas in a bicycle pump:
Push the pump in quickly - the gas heats up – you are doing work
on the gas.
Pull the pump out quickly - gas will cool down - the gas is doing
work for you.
On a molecular scale.
The gas particles are moving with a speed that is determined by the
temperature of the gas:
Push the pump in - the particles speed up - when they collide with
the oncoming piston, they rebound more quickly - they heat up.
Pull the pump out - the particles slow down - when they collide with
the outgoing piston, they rebound more slowly - they cool down.
ISNS 3371 - Phenomena of Nature
The same reasoning works for a gas that is expanding freely. Rather than
bouncing off a container, the particles bounce off each other. But they are
all moving outwards. So any collisions at the edges of the gas will have the
effect of taking some of the speed off the expanding molecules. Explains
why fog formed in chamber when pressure suddenly reduced:
All air contains water vapor of varying quantities. A state of saturation exists
when the air is holding the maximum amount of water vapor possible at the
existing temperature and pressure.
Dew point - the temperature to which the air would have to cool in order to
reach saturation - indicates the amount of moisture in the air. Condensation
of water vapor begins when the temperature of air is lowered to its dew
point and beyond - results in the formation of tiny water droplets that leads
to the development of fog, frost, clouds, or even precipitation.
When the air in the chamber suddenly expands, the temperature of the air
is suddenly reduced to below the dew point and the water vapor condenses
to form fog in the chamber.
Why is your breath colder when blown out through pursed lips?
ISNS 3371 - Phenomena of Nature
Bernoulli Effect
For horizontal fluid flow, an increase in the velocity of flow will result
in a decrease in the static pressure.
ISNS 3371 - Phenomena of Nature
The Airfoil (Wing) and the Bernoulli Effect
The air across the top of the airfoil
experiences increased air speed
relative to the wing - it must go farther
to reach the back edge of the airfoil.
This causes a decreases in pressure
and provides a lift force.
Increasing the angle of attack gives a
larger lift from the upward component
of pressure on the bottom of the wing.
The lift force can be considered to be a
Newton's 3rd law reaction force to the
force exerted downward on the air by
the wing.
At too high an angle of attack,
turbulent flow increases the drag
dramatically and will stall the aircraft.
ISNS 3371 - Phenomena of Nature
How Does an Airplane Fly Upside Down?
If the greater curvature on top of the wing and the Bernoulli effect are evoked
to explain lift, how is this possible? An increase in airstream velocity over the
top of the wing can be achieved with airfoil surface in the upright or inverted
position - requires adjustment of the angle of attack. Typical asymmetric
shape of airfoil increases efficiency of lift production but not essential for
producing lift.
ISNS 3371 - Phenomena of Nature
The Curve Ball and the Bernoulli Effect
A non-spinning baseball or a
stationary baseball in an
airstream exhibits symmetric
flow.
A baseball which is thrown with
spin will curve because the air
flows faster on one side of the
ball than the other side because
of friction. So one side of the
ball will experience a reduced
pressure.
The roughness of the ball's
surface and the laces on the
ball are important! With a
perfectly smooth ball you would
not get enough interaction with
the air.
ISNS 3371 - Phenomena of Nature
Balancing Ball and the Bernoulli Effect
A ball balances on a stream of air
because of the Bernoulli effect.
If the ball is displaced from the
center of the air stream, it will feel
a force pulling it back into the
center. The air on the right side of
the ball in not moving so pressure
is lower on the left side of the ball
and the ball feels a force toward
the center of the air stream.
No matter which direction the ball
is deflected, it is attracted to the
center of the air stream, and stays
balanced.