Chapter 20 Entropy and the Second Law of Thermodynamics

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Chapter 20Entropy and the Second Law of
Thermodynamics
20.1 Some one-way processes Which is closer to
common sense? Ink diffusing in a beaker of
water or diffused ink in a beaker concentrating
out of solution?? Although we would not be
violating energy conservation, we would be
violating the postulate for the change in
entropy, which states For an irreversible
process in a closed system, the entropy always
increases. What is entropy? Entropy is a state
function which is a measure of the disorder in a
system. Highly disordered systems (e.g. gases)
have more entropy than ordered systems (e.g.
solid crystals).
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The world behaves as if we can not treat work and
heat on an equal footing!! 20.3 Change in
entropy Actually, strictly speaking, all real
macroscopic processes are irreversible!! Many
real processes are very close to being
reversible. Reversibility of processes are only
an approximation!! A process is almost reversible
when it occurs very slowly so that the system is
virtually always in equilibrium (e.g. adding
grains to a piston in isothermal
contact). Entropy is a state variable. To
calculate the change in entropy between any two
states (i f) 1- Find a reversible process
between initial and final states. 2- Calculate
dS dQr/T for infinitesimal steps in the process.
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3- Take the integral between initial and final
states DS i?f dQr/T It is crucial to
distinguish between Q and Qr. What if the process
is irreversible?! It does not matter!! Entropy is
a state function. It depends on the state not the
process!! CP 1 Problem 20-1 Special cases 1-
Reversible process for an ideal gas DS n R
ln(Vf/Vi) n cv ln(Tf/Ti) 2- Melting DS m
LF/Tm 3- DS for a reversible adiabatic process
zero! 4- DS for (an arbitrary) cyclic process
ZERO!!
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5- Heat conduction DS Q/TL - Q/TH 6-
Adiabatic (isolated) free expansion DS n R
ln(Vf/Vi) 7- Irreversible heat transfer (w/o
mixing) DS m1c1ln(Tf/T1) m2c2ln(Tf/T2)
20-4 Second law of thermodynamic If a process
occurs in a closed system, the entropy of the
system increases for irreversible processes and
remains constant for reversible processes. That
is, the entropy of a closed system never
decreases. DSclosed DSsys DSres gt
0 irreversible DSclosed DSsys DSres
0 reversible Notice that isolated systems tend
toward disorder i.e. the entropy of the universe
increases in all natural processes.
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Can the entropy of a (particular) system ever
decrease? Yes!! but only at the expense of (at
least an equal) increase in another system. 20-5
Entropy in the real world Engines Heat engine/
engine/ working substance/ cycle/ strokes/
diagram with Q,T,W. Ideal engine is an engine in
which all processes are reversible and no
wasteful energy transfers occur due to friction
or turbulence or otherwise. Note Real engines
are not ideal, but very good engines are
approximately ideal. A Carnot engine is an ideal
engine, the cycle of which consists of four
strokes two idiabatics and two isothermals. How
does this look on a P-V diagram? How does this
look on a T-S diagram?
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Note that for a Carnot engine (can you prove
this?) TH/TL QH/ QL How do we calculate
the work of a Carnot cycle? Wc QH - QL
area inside the T-S cycle. Efficiency (e) of an
engine is defined to be e W/ QH For a Carnot
engine, the efficiency (ec) is ec W/ QH 1-
QL/ QH 1- TL/ TH How can one increase the
efficiency? Note that since TL gt 0 and TH lt 8 ,
ec is always less the unity. Therefore Even the
ideal engine is not perfect!! Real engines have
even lower efficiencies (e lt 40 ) than that of
Carnots.
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One way to express the second law of
thermodynamic is that It is impossible for a
machine to transfer thermal energy completely
into other forms of energy in any cyclic
process. Or, we can say Second law of
thermodynamic It is impossible to construct a
heat engine that, operating in a cycle, produces
no other effect than the absorption of thermal
energy from a reservoir and the performance of an
equal amount of work. (Kelvin-Plank
statement) 21-5 Entropy in the real world
Refrigerators Refrigerators and heat pumps are
heat engines running in reverse they move
thermal energy from a region at lower temperature
to a region at higher temperature (used for
cooling or heating). diagram Q,T,W Can this be
done with no work?! Work must be done on the
working substance.
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Coefficient of performance (COP or K) K Heat
transferred/ Work done For a refrigerator K
QL/W refrigerator Kc TL/(TH - TL)
refrigerator For a heater K QH/W heat
pump Kc TH/(TH - TL) heat pump Second law
of thermodynamic It is impossible to construct a
machine operating in a cycle that produces no
other effect than to transfer thermal energy
continuously from one object to another object at
a higher temperature. (Clausius statement)