Chapter 20 Entropy and the Second Law of Thermodynamics 20.1 Some one-way processes Which is closer...
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Transcript of Chapter 20 Entropy and the Second Law of Thermodynamics 20.1 Some one-way processes Which is closer...
![Page 1: 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.](https://reader036.fdocuments.us/reader036/viewer/2022081805/56649f2b5503460f94c46af3/html5/thumbnails/1.jpg)
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).
![Page 2: 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.](https://reader036.fdocuments.us/reader036/viewer/2022081805/56649f2b5503460f94c46af3/html5/thumbnails/2.jpg)
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.
![Page 3: 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.](https://reader036.fdocuments.us/reader036/viewer/2022081805/56649f2b5503460f94c46af3/html5/thumbnails/3.jpg)
3- Take the integral between initial and final states:
S = if 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:S = n R ln(Vf/Vi) + n cv ln(Tf/Ti)
2- Melting:S = m LF/Tm
3- S for a reversible adiabatic process: zero!
4- S for (an arbitrary) cyclic process: ZERO!!
![Page 4: 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.](https://reader036.fdocuments.us/reader036/viewer/2022081805/56649f2b5503460f94c46af3/html5/thumbnails/4.jpg)
5- Heat conduction: S = Q/TL - Q/TH
6- Adiabatic (isolated) free expansion:S = n R ln(Vf/Vi)
7- Irreversible heat transfer (w/o mixing):S = 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.
Sclosed = Ssys + Sres > 0 [irreversible]
Sclosed = Ssys + Sres = 0 [reversible]
Notice that isolated systems tend toward disorder; i.e. the entropy of the universe increases in all natural processes.
![Page 5: 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.](https://reader036.fdocuments.us/reader036/viewer/2022081805/56649f2b5503460f94c46af3/html5/thumbnails/5.jpg)
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?
![Page 6: 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.](https://reader036.fdocuments.us/reader036/viewer/2022081805/56649f2b5503460f94c46af3/html5/thumbnails/6.jpg)
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.
![Page 7: 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.](https://reader036.fdocuments.us/reader036/viewer/2022081805/56649f2b5503460f94c46af3/html5/thumbnails/7.jpg)
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 RefrigeratorsRefrigerators 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.
![Page 8: 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.](https://reader036.fdocuments.us/reader036/viewer/2022081805/56649f2b5503460f94c46af3/html5/thumbnails/8.jpg)
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)