# Physics 101: Lecture 31 Thermodynamics, part 2 - PowerPoint PPT Presentation

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## Physics 101: Lecture 31 Thermodynamics, part 2

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### Review of 1st law of thermodynamics. 2nd Law of Thermodynamics. Engines ... U depends only on T (U = 3nRT/2 = 3PV/2) Point on P-V plot ... Escher 'Waterfall' ... – PowerPoint PPT presentation

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Title: Physics 101: Lecture 31 Thermodynamics, part 2

1
Physics 101 Lecture 31Thermodynamics, part 2
• Review of 1st law of thermodynamics
• 2nd Law of Thermodynamics
• Engines and Refrigerators
• The Carnot Cycle

2
Quick Review
• 1st Law of Thermodynamics
• energy conservation

Q DU W
P
• U depends only on T (U 3nRT/2 3PV/2)
• Point on P-V plot completely specifies
• state of system (PV nRT)
• work done is area under curve
• for complete cycle
• DU0 ? QW

V
3
Second Law of Thermodynamics
• Not all processes that are allowed by energy
conservation occur in nature. Why ?
• Example
• Stone falls from height h
• mgh -gt ½ m v2 (just before impact) -gt heat
(contact with floor)
• This process is consistent with energy
conservation.
• The reversed process
• Stone lying on floor cools down and moves upward
to height h,
• has never been observed in nature, although it is
also allowed by
• energy conservation Q-gt1/2 mv2-gtmgh
• Or Ice melts but water does not spontaneously
freeze,
• heat flows from hot to cold but never from cold
to hot.
• We need a new concept which makes these
(reversed) processes
• highly unlikely.

4
New concept Entropy (S)
• A measure of disorder or probability of state
of a system.
• A property of a system (state function, just
like P, V, T, U)
• related to number of different states of system
• Examples of increasing entropy
• ice cube melts
• gases expand into vacuum
• Change in entropy
• ?S Q/T (T in K !) SI unit J/K
• gt0 if heat flows into system (Qgt0)
• lt0 if heat flows out of system (Qlt0)

5
Reversible vs. Irreversible changes in a
thermodynamic system
• Reversible changes are conceived to be those that
would occur very
• slowly, giving all the molecules in the
system time to 'adjust' to new
• conditions, and all state variables time to
• uniform throughout a system. Theoretically
you could imagine
• stopping at any point and reversing the
change slowly, recovering the
• previous thermodynamic state.
• Definition given by Fermi (1936), in
Thermodynamics
• "A transformation is said to be reversible when
the successive states
• of the transformation differ by infinitesimals
from equilibrium
• states.
• DSrev
0
• Irreversible Processes in which new entropy is
created. A system
• spontaneously changes, or energy is
transformed in a way that creates
• new entropy. This does not allow complete
recovery of all aspects
• of previous thermodynamic states.

• DSirrev gt 0
• Processes that happen spontaneously are
irreversible.

6
1st and 2nd Law of Thermodynamics A Perpetuum
Mobile (perpetual motion) of 1st and 2nd kind is
impossible.
Or The energy of the universe is constant, the
entropy of the universe seeks to be maximal.
R.Clausius
(1822-1888) Perpetuum Mobile of 1st kind A
machine that is able to provide useful work
without input of external energy (e.g. heat) and
without change of the physical or chemical status
of its parts does not exist (or a machine that
creates energy continuously does not exist).
Perpetuum Mobile of 2nd kind A machine
undergoing a cyclic process which does nothing
more than convert heat into mechanical (or other)
work does not exist.
M.C. Escher Waterfall (1961)
7
Second Law of Thermodynamics
• The entropy change (Q/T) of the
systemenvironment ? 0
• never lt 0
• order to disorder
• The entropy of the universe increases whenever an
irreversible process occurs. All real processes
in nature are irreversible.
• Consequences
• A disordered state cannot spontaneously
transform into an more ordered state.
• No engine operating between two reservoirs can be
more efficient than one that produces zero change
in entropy. The latter is called a Carnot
engine (no real engine can ever be perfectly
reversible but Carnot is a useful idealization,
since
• it represents the limiting case) .
• Heat cannot be transferred spontaneously from
cold to hot.

8
Engines and Refrigerators
• System taken in closed cycle ? ?Usystem 0
• Therefore, net heat absorbed work done
• QH - QC W (engine)
• QC - QH -W (refrigerator)
• energy going into green blob energy leaving
green blob

9
The objective turn heat from hot reservoir (QH)
into work The cost heat is wasted 1st Law
QH -QC W efficiency e ? W/QH W/QH
(QH-QC)/QH 1-QC/QH
10
The objective remove heat from cold reservoir
(QC) The cost work needs to be done 1st Law
QH W QC coefficient of performance CPr
? QC/W QC/W QC/(QH - QC)
11
Engines and the 2nd Law
The objective turn heat from hot reservoir into
work. The cost heat is wasted 1st Law QH
-QC W efficiency e ? W/QH W/QH 1-QC/QH
?S QC/TC - QH/TH ? 0 ?S 0 for
Carnot Therefore, QC/QH ? TC/ TH QC/QH TC/ TH
for Carnot Therefore e 1 - QC/QH ? 1 - TC/ TH
e 1 - TC/ TH for Carnot gt efficiency
of a realistic engine can never be larger than
eCarnot ! e largest if TC ltlt TH
12
Concept Question
Consider a hypothetical device that takes 1000 J
of heat from a hot reservoir at 300K, ejects 200
J of heat to a cold reservoir at 100K, and
produces 800 J of work. Does this device violate
the first law of thermodynamics ? 1. Yes 2. No
This device doesn't violate the first law of
thermodynamics because no energy is being created
nor destroyed. All the energy is conserved.
• W (800) Qhot (1000) - Qcold (200)
• Efficiency W/Qhot 800/1000 80

13
Concept Question
Consider a hypothetical device that takes 1000 J
of heat from a hot reservoir at 300K, ejects 200
J of heat to a cold reservoir at 100K, and
produces 800 J of work. Does this device violate
the second law of thermodynamics ? 1. Yes 2. No
• W (800) Qhot (1000) - Qcold (200)
• Efficiency W/Qhot 800/1000 80
• Max eff 1 - 100/300 67 eCarnot
• e gt eCarnot is forbidden by second law
• D S DSHDSC200/100 J/K 1000/300 J/K lt 0

.
14
Concept Question
• Consider a hypothetical refrigerator that takes
1000 J of heat from a cold reservoir at 100K and
ejects 1200 J of heat to a hot reservoir at 300K.
• How much work does the refrigerator do?
• 2. What happens to the entropy of the universe?
• 3. Does this violate the 2nd law of
thermodynamics?

QC 1000 J QH 1200 J
Since QC W QH, W 200 J
DSH QH/TH (1200 J) / (300 K) 4 J/K
DSC -QC/TC (-1000 J) / (100 K) -10 J/K
DSTOTAL DSH DSC -6 J/K ? decreases
(violates 2nd law)
15
Heat Capacities of an Ideal Gas
• As discussed in Chapter 12, the heat needed to
raise the
• temperature of a solid or liquid is given by
Qcm DT
• where c is the heat capacity of the material.
• Gases Volume and/or pressure change when
temperature changes (this effect can be safely
neglected in case of solids and liquids).
• Heat capacity of a gas depends on if T changes
• at constant V, cV, or constant P, cP,
• Vconst. DUQcV m DT3/2 n R DT gt CVcVm/n
3/2 R
• Pconst. DUQ-PDVcP m DT-n R DT3/2 n R DT
• gt CPcP m/n 5/2 R
• CV and CP are the molar specific heat capacities
of an ideal
• monatomic gas.