THERMODYNAMICS
ZEROTH LAW OF THERMODYNAMICS
If two objects are
each in equilibrium
with a third object,
they are also in
thermal equilibrium
with each other.
AVERAGE TRANSLATIONAL KE
 Notice that the kinetic energy of the molecule
only depends on temperature
 The temperature of a gas is a direct
representation of the average energy of the
molecules in the gas
AVERAGE KINETIC ENERGY
 Kinetic Molecular Theory: There’s a huge number
of molecules.
 Practical Application: We need to use the average
speed to find the kinetic energy. Find it from the
equation for the average molecular kinetic energy:
ROOT MEAN SQUARE SPEED
 It’s exactly what you’d expect with a couple notes
• μis the mass of the molecule
• Boltzmann Constant vs. the Universal Gas Constant
 On the AP equation sheet:
CHEMISTRY REVIEW
 Universal Gas Constant vs. Boltzmann Constant
• Boltzmann decided it would be useful if we knew
what the gas constant was per molecule instead of per
mole
R
kb =
N0
• Does it work?
UNIT WARNING
 Unlike chemistry
• Temperature is always measured in Kelvin
K = oC + 273.15
• Molar Mass must be in kg/mol
FIRST LAW OF THERMODYNAMICS
 Conservation of energy, but this time with
respect to gases in the kinetic theory of ideal
gases
• Adding heat and doing work on a gas increases its
internal energy
• Removing heat and allowing the gas to do work
decreases its internal energy
INTERNAL ENERGY OF A SUBSTANCE
 A convenient model is that
atoms vibrate like they’re
connected by springs
• Kinetic energy as they
oscillate
• Potential energy that
binds them together
INTERNAL ENERGY
 All gas has a certain amount of internal energy
 At a MICROSCOPIC level, not macroscopic
DU =U f -Ui
 ΔU is positive when internal energy increases
HEAT



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Heat is the transfer of energy, not energy itself
Units: Joules
Symbol: Q
If we add heat to a system, we are really adding
energy to its internal energy
• Q is positive when work is done on the system
• Q is negative when work is removed from the system
We’re back to Work1
 Work can be performed on gases
• Example: Push down on the piston of a cylinder
of gas, reducing its volume.
• If we smush the molecules together like this,
then we are increasing the collisions that will
happen in that smaller volume. Doing work on
the gas increases the internal energy.
• Work is positive when it is done on a system.
Footnote: 1 Pun intended
We’re back to Work1
 Gases can do Work
• Example: the gas pushes the cylinder
back up, increasing its volume.
• In this case the gas has done the work,
so the internal energy of the gas
decreased.
• Work is negative when it is done by the
system
FIRST LAW OF THERMODYNAMICS
 We measure how much we changed the internal
energy of the system by adding/removing heat
and doing work on/by the gas.
IDEAL GAS LAW
 Show that these two forms are equivalent
 Boyle’s Law is just
one implication of
the Ideal Gas Law
PV DIAGRAMS
 There are four different situations that you can
expect to see shown in PV diagrams:
1. Isobaric: the gas is held at a constant pressure
2. Isochoric: the gas is held at a constant volume
3. Isothermal: the gas is held at a constant temperature
4. Adiabatic: No heat flows in or out of the gas
Isobaric –What happens
 We place a heat source under a
cylinder
• Since this is an isobaric process, the
pressure must stay the same as it was
at the start.
• We also expect that with the extra internal
energy the molecules have gained from the
heat source, they will be bouncing around
a bit more.
• This must result in the gas expanding in
the cylinder
ISOBARIC PV DIAGRAM
 The PV diagram shows a gas going from a
smaller to a bigger volume, while the pressure
stays constant.
 Note: The area underneath the line is
PV = Work
ISOCHORIC
 In an isochoric process the gas must keep a
constant volume, so we will put the gas in a
sealed container that can not change size or shape.
 Pressure increases
 No Work done
 From the First Law: Since no Work is done, the
added heat just increases the internal energy
ISOCHORIC PV DIAGRAM
 This is consistent
• No area => no Work
 The Ideal Gas Law is
also consistent
• The pressure increase is due to
heat being added, which in turn
directly affect the internal
energy
ISOTHERMAL
 Temperature remains constant
• As the volume of a gas expands the pressure would need
to drop
 Work is being done by the gas (work is negative), so
to keep the internal energy (and temperature)
constant, the gas must be absorbing heat from the
water.
 As long as the energy lost (by the gas doing work)
equals the heat gained from the water, the internal
energy will not change and the temperature stays the
same.
ISOTHERMAL PV DIAGRAM
 Pressure and volume both change
 Line of constant temperature called an isotherm
 Area underneath is the Work done, but you can’t
find it without calculus since it’s curved
ADIABATIC
 No heat is added to the system
 This is NOT the same as isothermal, the
temperature can change
 Q = 0 J, so according to the First Law
• If the gas is compressed (work done on the gas is positive) the
internal energy increases.
• If the gas expands (work done by the gas is negative) the
internal energy decreases.
ADIABATIC PV DIAGRAM
 Looks similar to isothermal, but drops off so it
must begin and end on different isotherms
 As we've already discussed, in the adiabatic
process where a gas expands, the work done by
the gas causes the internal energy to decrease, so
the temperature must decrease as well.
INTERNAL ENERGY AGAIN
 Since ΔU = W for an adiabatic process, if we
figure out the initial and final internal energies, we
can figure out the work done on or by the gas
without having to use calculus to figure out the
area under the PV curve.
 The following is not on your equation sheet:
SUMMARY OF PROCESSES
SECOND LAW OF THERMODYNAMICS
 Heat will always spontaneously flow from a
hotter to a colder object.
 Or, in physics speak:
 The entropy of a closed system shall never
decrease and shall increase whenever possible.
ENTROPY
 Entropy is a measure of the disorder of a system.
 All systems tend toward an increase in entropy
unless Work is done on them
HEAT ENGINES
 A heat engine uses energy to perform work
• The heat that is the input to run the engine
comes from an area at a higher temperature,
called a hot reservoir.
• Some of the input is used to do some actual
work. This is the output that we actually
want.
• The rest of the heat is released (basically as
waste) to a cold reservoir.
HEAT ENGINES
 This obeys the 1st and 2nd laws
• The input heat is equal to the Work done plus the
heat released (1st law)
• The heat is flowing from the hot to cold reservoir (2nd
Law)
EFFICIENCY
 The more Work an engine produces from the
input heat, the more efficient the engine
 Efficiency is found by dividing
• W: the work done, by
• QH: the input heat from the hot reservior
EFFICIENCY EQUATION #2
 Using the notation of
• QH as the input heat from the hot reservoir
• QC as heat flowing to the cold reservior
 The first law can be rewritten
QH = W + Q C
 Which we can rearrange if we want to
W = Q H - QC
EFFICIENCY EQUATION #2
 A heat engine is running with an input of heat of
1.45 x 104 J. If it dumps 1.02 x 104 J of waste
heat into its surroundings, determine the
efficiency of the engine.
 Combining this equation for the first law with the
equation for efficiency
QC
e = 1QH
CARNOT HEAT ENGINE
 By the early 1800s scientist were asking if there
were a limit to how efficient an engine could be
 Sadi Carnot proved the efficiency, he said
• The heat engine reaches its maximum efficiency when
all of the steps are reversible
• Reversible means that the engine (the system) and
everything around it (the surroundings) can return to
the same state they were in before the engine was
running
• Friction gets in the way of real life engines being
reversible and the second law can also
CARNOT ENGINE
Is useful despite
not actually being
possible since
every real world
engine must be
less than the
Carnot engine
efficiency for the
same situation
CARNOT ENGINE
 The best possible engine would be one that did
the most work based on the temperature
difference that it had available between the two
reservoir
 It can be shown that the ratio of the heat of the
two reservoirs is equivalent to the ratio of their
temperatures.
CARNOT ENGINE
 We can substitute this into the second equation
for efficiency we came up with
 Even in Carnot's perfectly reversible engine, there
must be a difference in temperature between the
two reservoirs, so that heat can flow on its own
REFRIGERATORS AND HEAT PUMPS
 Heat won’t flow on its own
from cold to hot, but we
can force it to!
 A refrigerator is a heat
engine in reverse, we do
work to move heat from a
cold reservoir to a hot
reservoir
 Can you think of another
example?
HEAT PUMP
 A heat pump is a device that works like a
refrigerator, except that it is used to heat a
building in cold weather.
• For a heat pump, the cold reservoir is the
outdoors, and the hot reservoir is the
inside of the building.
• Electricity is used to do the work of
pumping the heat.