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  3. Unit 1. thermodynamics
  4. The second law of thermodynamics
  5. Entropy on a microscopic scale

4.7 Entropy on a microscopic scale  (Page 4/10)

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Check Your Understanding A quantity of heat Q is absorbed from a reservoir at a temperature T h by a cooler reservoir at a temperature T c . What is the entropy change of the hot reservoir, the cold reservoir, and the universe?

− Q / T h ; Q / T c ; and Q ( T h − T c ) / ( T h T c )

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Check Your Understanding A 50-g copper piece at a temperature of 20 °C is placed into a large insulated vat of water at 100 °C . (a) What is the entropy change of the copper piece when it reaches thermal equilibrium with the water? (b) What is the entropy change of the water? (c) What is the entropy change of the universe?

a. 4.71 J/K; b. −4.18 J/K; c. 0.53 J/K

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View this site to learn about entropy and microstates. Start with a large barrier in the middle and 1000 molecules in only the left chamber. What is the total entropy of the system? Now remove the barrier and let the molecules travel from the left to the right hand side? What is the total entropy of the system now? Lastly, add heat and note what happens to the temperature. Did this increase entropy of the system?

Summary

  • Entropy can be related to how disordered a system is—the more it is disordered, the higher is its entropy. In any irreversible process, the universe becomes more disordered.
  • According to the third law of thermodynamics, absolute zero temperature is unreachable.

Key equations

Result of energy conservation W = Q h − Q c
Efficiency of a heat engine e = W Q h = 1 − Q c Q h
Coefficient of performance of a refrigerator K R = Q c W = Q c Q h − Q c
Coefficient of performance of a heat pump K P = Q h W = Q h Q h − Q c
Resulting efficiency of a Carnot cycle e = 1 − T c T h
Performance coefficient of a reversible refrigerator K R = T c T h − T c
Performance coefficient of a reversible heat pump K P = T h T h − T c
Entropy of a system undergoing a reversible process at a constant temperature Δ S = Q T
Change of entropy of a system under a reversible process Δ S = S B − S A = ∫ A B d Q / T
Entropy of a system undergoing any complete reversible cyclic process ∮ d S = ∮ d Q T = 0
Change of entropy of a closed system under an irreversible process Δ S ≥ 0
Change in entropy of the system along an isotherm lim T → 0 ( Δ S ) T = 0

Conceptual questions

Are the entropy changes of the systems in the following processes positive or negative? (a) water vapor that condenses on a cold surface; (b) gas in a container that leaks into the surrounding atmosphere; (c) an ice cube that melts in a glass of lukewarm water; (d) the lukewarm water of part (c); (e) a real heat engine performing a cycle; (f) food cooled in a refrigerator.

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Discuss the entropy changes in the systems of Question 21.10 in terms of disorder.

Entropy is a function of disorder, so all the answers apply here as well.

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Problems

A copper rod of cross-sectional area 5.0 cm 2 and length 5.0 m conducts heat from a heat reservoir at 373 K to one at 273 K. What is the time rate of change of the universe’s entropy for this process?

3.78 × 10 −3 W/K

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Fifty grams of water at 20 °C is heated until it becomes vapor at 100 °C . Calculate the change in entropy of the water in this process.

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Fifty grams of water at 0 °C are changed into vapor at 100 °C . What is the change in entropy of the water in this process?

430 J/K

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
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John Reply
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Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
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David Reply
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David
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emma Reply
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what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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Adjanou
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Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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Maurice
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Magreth
progressive wave
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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