2nd Law

1
Thermodynamics 2

• 2nd Law
• Cycles
• Efficiency
• Heat engines and refrigerators
• Entropy
• Kinetic theory of gasses
• Maxwells demon
• Tipler Chapters 18,19,20

Dr Mervyn Roy, S6
2
2nd Law
Some processes are allowed by the first law, but
never happen
We must be missing something!
3
Cyclic process
We can extract useful work from a cycle
Work out
Work in
Work extracted
W W1 - W2
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Efficiency
1st Law Q ?U W
P
Q2
Q1
W1
In one complete cycle ?U 0 Heat in work
extracted Heat out Q1 Q2 (W1W2 )
Q3Q4 Qin W Qout
Q3
Q4
W2
V
Efficiency W / Qin
5
Heat engine
Qh W Qc Efficiency W / Qh
6
Refrigerator
Heat engine
W Qc Qh COP Qc / W
Qh W Qc Efficiency W / Qh
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2nd Law
Perfect refrigerator
Hot reservoir (Th)
Qh
W0 QcQh
Qc
Cold reservoir (Tc)
Not allowed!
It is impossible for a refrigerator working in a
cycle to produce no other effect than the
transfer of thermal energy from a cold object to
a hot object.
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2nd Law
Perfect refrigerator
Perfect heat engine
Hot reservoir (Th)
Hot reservoir (Th)
Qh
Qh
W0 QcQh
W
Qc0, QhW
Qc
Cold reservoir (Tc)
Cold reservoir (Tc)
Not allowed!
Not allowed!
It is impossible for a refrigerator working in a
cycle to produce no other effect than the
transfer of thermal energy from a cold object to
a hot object.
It is impossible for a heat engine working in a
cycle to produce no other effect than that of
extracting thermal energy from a reservoir and
performing an equivalent amount of work.
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Entropy
In any irreversible process the system plus its
surroundings move to a less ordered state. Less
ordered means the ability to do work has been
lost.
Entropy, S, measures disorder. S is a state
variable like U, P, V, T etc.
For any process the entropy of the universe never
decreases
10
Highest efficiency possible?
P
Carnot engine Most efficient engine that can
operate between two thermal reservoirs.
Qin
adiabatic
isothermal
Efficiency 1 - Qout/ Qin Highest efficiency
possible 1 TC / Th e.g. Steam Engine.
Efficiency 1 273/373
adiabatic
Qout
isothermal
V
SeaGen 1.2 MW from tides in and out of
Strangford Lough (N.I.) through the Narrows. The
turbine rotor blades can be pitched through
180 degrees allowing them to operate in both flow
directions on ebb and flood tides.
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Feel the Entropy!
1st Law W dU Q
Ideal gas
Ideal gas
Area A
F
piston
Elastic band
12
Kinetic Theory
Have related microscopic motion to macroscopic
variables!
Relates temperature to average molecular speed
Equipartition of Energy energy shared equally
(kT/2) between all DOF (explains value of cv in
an ideal gas)
13
Maxwell-Boltzman distribution

• not all molecules in a gas have the same speed
• distribution of speeds, , from
  statistical mechanics

dv
14
Maxwell-Boltzman distribution

• Hydrogen, mmp

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Maxwell-Boltzman distribution

• Hydrogen, mmp

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Maxwell-Boltzman distribution

• Hydrogen, mmp

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2nd Law
2nd law is valid statistically High order low
probability Low order high probability
is possible, it is just highly improbable
the larger (more macroscopic) the system, the
more improbable.
10 molecules, P1/1024. 20 molecules, P1/1048576.
18
Maxwells Demon
19
Maxwells Demon
20
PA2001 Time and Energy
Maxwells Demon
?
Thermodynamics
21
PA2001 Time and Energy
Maxwells Demon
Thermodynamics