Transcript Document 7347997

Chapter 20
Entropy 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).
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.
3- Take the integral between initial and final
states:
f
DS = i 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!!
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 > 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.
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?
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 > 0 and TH < ∞ , ec is always
less the unity. Therefore:
Even the ideal engine is not “perfect”!!
Real engines have even lower efficiencies (e ~< 40
%) than that of Carnot’s.
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.
Coefficient of performance (COP or K):
K =Heat transferred/ Work done
For a refrigerator:
K = QL/W
Kc = TL/(TH - TL)
[refrigerator]
[refrigerator]
For a heater:
K = |QH|/W
Kc = TH/(TH - TL)
[heat pump]
[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)