# Homework Help: True/False: Qualitative Thermodynamics Question

1. Dec 19, 2012

### yaylee

1. The problem statement, all variables and given/known data

Which of the following statements about entropy and heat engines are true? (There is more than one right answer!)

1)The entropy of the universe can never decrease
2) The COP (coefficient of performance) of a refrigerator can never be greater than 1
3) All Carnot engines are reversible
4) A refrigerator lowers the entropy of the volume inside
5) If the temperature of the cold reservoir increases with the temperature of the hot reservoir unchanged, the efficiency of a Carnot engine will increase
6) Any process that includes adding heat to an ideal gas will increase the entropy of the gas
7)It is impossible have a net transfer of heat from a cold reservoir to a warm reservoir
8) All Carnot engines are more efficient than all real engines
9) All heat engines operating between the same temperatures have the same efficiency
10)Adiabatic expansion will lower the temperature of a gas
11) The entropy of a system can never decrease
12) The efficiency of a Carnot engine can never be 1

2. Relevant equations
Entropy = dQ/T
efficiency of Carnot Engine = 1 - (Tc/Th), where Tc = Temp of cold reservoir, Th = hot.
Coefficient of Performance C.O.P = Qc/W, where Qc = heat absorbed into cold reservoir
Work done in ANY cycle, W = Qh - Qc.

3. The attempt at a solution
Note: I bolded the correct answer, with explanation below the correct statement!
1)The entropy of the universe can never decrease
By definition, entropy will be equal to 0 in a Carnot cycle, greater than 0 in a real cycle..
2) The COP (coefficient of performance) of a refrigerator can never be greater than 1
3) All Carnot engines are reversible
By definition, Carnot engines are quasi-static, reversible processes.
4) A refrigerator lowers the entropy of the volume inside
Decreasing entropy is analagous to saying you are "removing heat" from the refrigerator.
5) If the temperature of the cold reservoir increases with the temperature of the hot reservoir unchanged, the efficiency of a Carnot engine will increase
e = 1 - Tc/Th. Increasing Tc will decrease e.
6) Any process that includes adding heat to an ideal gas will increase the entropy of the gas
By definition, dS = +dQ/T, so dS is positive.
7)It is impossible have a net transfer of heat from a cold reservoir to a warm reservoir
8) All Carnot engines are more efficient than all real engines
Simple definition.
9) All heat engines operating between the same temperatures have the same efficiency
10)Adiabatic expansion will lower the temperature of a gas
11) The entropy of a system can never decrease
Simple definition.
12) The efficiency of a Carnot engine can never be 1
At absolute zero, this will be true.

Pls point out where I may have missed a true statement, or marked a true statement which is actually false. Many thanks in advance for your help! Infinite appreciation !

2. Dec 23, 2012

### Raindrop13

1) True, because it’s the whole system.
2) False. http://wiki.answers.com/Q/Why_coefficient_of_performance_of_a_refrigerator_is_greater_than_1
3)True
4)True
5)True. Imagine the difference between a refridgerator and a freezer.
6) "Yes, thermodynamically. In statistical mechanics heat increases the number of microstates and thus entropy which is proportional to their log." quoted from anna v, http://physics.stackexchange.com/q/47435/11833 [Broken]
You can refer to this too https://www.physicsforums.com/showthread.php?t=177049
7)False. That’s what refridgerators do.
8)True.
9)False. For example, Carnot is the most efficient.
10) True. In adiabiatic, $$Q=0, TV^{\gamma -1}=constant$$ and $$PV^{\gamma }=constant[/tex ] 11) True 12)True. Your explanation is wrong: (When [tex]T_c$$ is) At absolute zero, this will be false.

All your true/false is correct. Lol why do you even ask.

Last edited by a moderator: May 6, 2017
3. Dec 24, 2012

### Andrew Mason

My answers are in italics:

1)The entropy of the universe can never decrease. True

2) The COP (coefficient of performance) of a refrigerator can never be greater than 1 False

3) All Carnot engines are reversible True or False depending on whether you include external mechanical irreversibility. An engine operating on the Carnot cycle but whose output work is dissipated due to friction is not reversible.

4) A refrigerator lowers the entropy of the volume inside True

5) If the temperature of the cold reservoir increases with the temperature of the hot reservoir unchanged, the efficiency of a Carnot engine will increase False. Efficiency will decrease (Efficiency = 1-Tc/Th).

6) Any process that includes adding heat to an ideal gas will increase the entropy of the gas True

7)It is impossible have a net transfer of heat from a cold reservoir to a warm reservoir True or False, depending on what it means by "net" transfer of heat. If "net" refers to the transfer of heat in the Clausius statement of the second law: "No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.", then the statement is true. .

8) All Carnot engines are more efficient than all real engines False. It depends on the temperatures the engines operate between.

9) All heat engines operating between the same temperatures have the same efficiency False. This is true only for all Carnot engines operating between the same temperatures

10)Adiabatic expansion will lower the temperature of a gas False. An adiabatic free expansion of an ideal gas results in no change in temperature.

11) The entropy of a system can never decrease False. The entropy of the system + surroundings can never decrease

12) The efficiency of a Carnot engine can never be 1True but it can get arbitrarily close to 1 as Tc → 0K. Absolute 0 is unattainable even in theory.

AM

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