Chapter 18 Heat and the First Law of Thermodynamics

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```					  Chapter 18: Heat and the
First Law of Thermodynamics

Prof. Chris Wiebe
Prof. Simon Capstick

ΔE = Q + W

“Lisa’s perpetual motion machine just keeps moving faster and faster!”
What is wrong with a perpetual motion machine?
PV diagram review
Remember, the work done
depends upon the path we
take and is equal to
W = -∫pdV.

A fixed amount of gas is
compressed from a
pressure Pi and a volume
Vi to a (smaller) volume Vf
and a (larger) pressure Pf.
Which method does more
work?
(1)   Path A
(2)   Path B
(3)   Path C
Answer: Path A has the largest area under the
PV curve – it has the largest work done
PV diagrams for the ideal gas
PV diagrams are useful because
they tell us how much work is done
or how much heat is released for a
certain process
We can look at the amount of work
that an engine does in a cycle
(starting and ending at the same
point on the PV curve). Engines
take heat and convert it to energy in                             Get work out
the form of work (which, for                                      of some of
example, moves a piston)                                          this heat
Be careful when calculating the                                   energy
work done or heat
absorbed/released! Work done by
you is positive, work done by the
gas is negative. Heat absorbed by
the gas is positive, heat taken away
from the gas is negative
For one cycle, the total amount of      A cycle is changing states from a-b-c-d
energy should be conserved              We take in heat when we go from b->c,
(otherwise you would make a             and release heat from d->a
perpetual motion machine!)
PRS Question
An ideal gas system changes from state i to state f
by paths iaf and ibf. If the heat added along iaf is
Qiaf = 50 cal, the work along iaf is Wiaf = 20 cal.
Along ibf, if Qibf = 40 cal, the work done, Wibf, is
A) 10 cal
B) 20 cal
C) 30 cal
D) 40 cal
E) 50 cal
Heat capacity of a gas
There are two ways that we can
raise the temperature of a gas:
(1) We can heat at constant
pressure (allow the piston to move)
(2) We can heat at constant volume
(fixed piston position)                       Constant pressure

At constant volume:
ΔEint = Q + Won = Q = CV ΔT
At constant pressure:
ΔEint = Q + Won = Q – P ΔV =CP ΔT – P ΔV

CV – heat capacity at constant volume
CP – heat capacity at constant pressure
Constant volume
Heat capacity of a gas
At constant volume (with
very small changes):
dEint /dT = CV   dEint = CV dT
At constant pressure:
dEint = CP dT – P dV
CV dT = CP dT – P dV
Ideal gas law:                   Constant pressure
PV = nRT
At constant pressure:
P dV = nR dT
CV dT = CP dT – nR dT

CP = CV + nR

Constant volume
Monatomic gases
The heat capacity is different for polyatomic
gases compared to monatomic.
Monatomic gas molecules can’t rotate so
the only degrees of freedom are
translational (moving in x, y, or z direction)
CV = dEint /dT = d[(3/2)nRT]/dT
= (3/2) nR
At constant pressure:
CP = CV + nR = (3/2) nR + nR
= (5/2) nR
Polyatomic gases
Polyatomic gases have extra
degrees of freedom, such as
vibration or rotation.
Diatomic molecules have Cv =
5/2 nR (more degrees of
freedom) at room temperature
Polyatomic molecules have
Cv = 7/2 nR (they can also
vibrate in two different
directions) at room
temperature
isobaric (constant P) and
isothermal (constant T)
processes
An adiabatic process is when Q
= 0 (the system is well insulated
and there is no net heat transfer
to the surroundings)
ΔE = Q + W = W. The
temperature, volume, and
pressure can change!
For this process: PVγ = constant
Here γ = CP/CV
Note CP = CV + nR, so
γ = 1 + nR/CV
the ideal gas law and the first law of thermodynamics!)
End of chapter

Practice problems:
25, 27, 29, 33, 35, 45, 49, 53, 59, 71,
73, 75
Neat stuff at the end of the chapter:
heat capacity of a solid, failure of the
equipartition theorem (not on the
exam)
Chapter 19: The Second Law
of Thermodynamics
Prof. Chris Wiebe
Prof. Simon Capstick

Ludwig Boltzmann (1844 – 1906)
S = k log W
Entropy and the Second Law
of Thermodynamics
The second law of thermodynamics tells us about entropy:
“The entropy of the universe (system plus its surroundings) can never decrease”
What is entropy?
Entropy (symbol: S) is a measure of disorder in a system
The total entropy tends to increase for any process
Entropy is sometimes called “Time’s Arrow”, because it tells us which way time flows
in physics equations – the entropy increases

An example of entropy with gas molecules
The situation on the left
corresponds to a more
ordered state than the right

If we let heat flow between
these two systems, the
resulting state is more
disordered – a random
distribution of speeds in both
containers (at the same T)
An example of entropy
Salt shaker demo
Drop of food coloring into water
Free expansion of a gas
One definition of entropy: ΔS =
ΔQ/T
For an isothermal expansion, ΔE =
ΔQ + W = 0. So ΔQ = -W              The free expansion of a gas
So ΔQ = nRT ln(Vf/Vi) and           is driven by the tendency for
ΔS = nR ln(Vf/Vi). The expansion     entropy to increase for any
of this gas is an example of the            given process
increase of entropy (it would be
odd if the molecules wouldn’t
expand out of the cylinder!)

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