# The entropy of the universe can never decrease

## Homework Statement

WHICH OF THESE IS TRUE:

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

## The Attempt at a Solution

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

Andrew Mason
Homework Helper

## The Attempt at a Solution

[*]Adiabatic expansion will lower the temperature of a gas (F)
This is true because the expansion will always do work. If no heat flows into the gas, and the gas does work, the internal energy - hence temperature - must decrease.

You may be thinking of free expansion. Theoretically, in an adiabatic expansion that is completely free (increase in volume at 0 external pressure) the gas would no work and therefore the temperature would not go down. But there can be no completely free expansion into a finite volume: as soon as some gas fills the volume it creates non-zero pressure, and the gas that enters afterward must expand against that pressure.
[*] If the temperature of the cold reservoir increases with the temperature of the hot reservoir unchanged, the efficiency of a Carnot engine will increase (T)
Efficiency would decrease if the temperature difference decreases.
[*]The efficiency of a Carnot engine can never be 1 (T)
Well, it can be arbitrarily close to 1 if the cold reservoir is arbitrarily close to absolute 0.
[*] The COP (coefficient of performance) of a refrigerator can never be greater than 1 (T)
Write out the definition of COP for a refrigerator. You are saying that the amount of heat removed from the cold reservoir cannot exceed the work done on the system. Why?

AM

Hey I tried your suggestions theres something else wrong...

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

Andrew Mason
Homework Helper

Try changing 2 (as explained in my first answer), and 8. (8 - Since one can never reach absolute 0, one can never actually reach an efficiency of 1)

AM

Yeah thats what I did... sorry about that, I must've gone wrong copiying and pasting... SO this is what I have at the moment and its wrong:

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

Everything not answered i marked false. The whole set of questions is treated as one problem so even if I go wrong with one I get it marked wrong

Thanks alot for your help, Im sorry I dont mean to be a pain, It's just Im so sure of the answers I've chosen I double checked read through the notes and the book... It's just frustrating

Andrew Mason
Homework Helper

The first question is a trick question. A Carnot engine operating between two temperatures is always more efficient than other heat engines operating between those same two temperatures. But that is not what the question asks, is it?

AM

Andrew Mason
Homework Helper

[*]All Carnot engines are more efficient than all real engines T

[*]If the temperature of the cold reservoir increases with the temperature of the hot reservoir unchanged, the efficiency of a Carnot engine will increase T
Check these.

[*]The COP (coefficient of performance) of a refrigerator can never be greater than 1
If the "1" is supposed to be a "T" you should reconsider. COP = Qc/W. Why can this not be greater than 1?

AM

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

I think I've implemented all the changes you proposed. And yet it says its wrong...

Andrew Mason
Homework Helper

1. The COP (coefficient of performance) of a refrigerator can never be greater than 1 (F) (F)
2. If the temperature of the cold reservoir increases with the temperature of the hot reservoir unchanged, the efficiency of a Carnot engine will increase (F) (F)
3. The entropy of a system can never decrease (F) (F)
4. Adiabatic expansion will lower the temperature of a gas (T) (F) (let's assume the exception is free expansion)
5. All heat engines operating between the same temperatures have the same efficiency (F) (F)
6. The efficiency of a Carnot engine can never be 1 (F) (F)
7. It is impossible have a net transfer of heat from a cold reservoir to a warm reservoir (F) (F)
8. The entropy of the universe can never decrease (T) (T)
9. All Carnot engines are reversible (T) (T)
10. A refrigerator lowers the entropy of the volume inside (T) (T)
11. Any process that includes adding heat to an ideal gas will increase the entropy of the gas (T) (F)
12. All Carnot engines are more efficient than all real engines (F) (F)

I think I've implemented all the changes you proposed. And yet it says its wrong...

You may wish to reconsider "Any process that includes adding heat to an ideal gas will increase the entropy of the gas ". The key word here may be "includes". There is a subtle distinction between "adding heat to a gas" (which increases entropy of the gas) and a 'process that includes adding heat to a gas'. A process that includes adding heat to a gas but which goes on to restore the gas to its original state does not increase the entropy of the gas. An example would be a cycle of a heat engine. Heat is added, work is done and the engine returns to its original state. No change in entropy.

With that, my answers are marked in Red. If that doesn't work you might want to change the answer for "Adiabatic expansion will lower the temperature of a gas" for the reasons discussed in my first post.

AM

It's still coming out wrong Andrew, I tried both what you posted and what you suggested about the adiabatic expansion.

THE FOLLOWING ARE WHAT I MARKED TRUE
1. Adiabatic expansion will lower the temperature of a gas
2. The entropy of the universe can never decrease
3. A refrigerator lowers the entropy of the volume inside
4. All Carnot engines are reversible

THE FOLLOWING I MARKED FALSE:
1. The efficiency of a Carnot engine can never be 1
2. All heat engines operating between the same temperatures have the same efficiency
3. All Carnot engines are more efficient than all real engines
4. The entropy of a system can never decrease
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. It is impossible have a net transfer of heat from a cold reservoir to a warm reservoir
7. The COP (coefficient of performance) of a refrigerator can never be greater than 1
8. Any process that includes adding heat to an ideal gas will increase the entropy of the gas
And as I said I tried "Adiabatic expansion will lower the temperature of a gas" both as true and false and the whole set was marked wrong

Andrew Mason
Homework Helper

Try changing: The efficiency of a Carnot engine can never be 1 to (T). As previously discussed, this is somewhat ambiguous.

Also: Adiabatic expansion will lower the temperature of a gas (F) (free expansion).

If that doesn't work, try different combinations of the other ambiguous ones.

AM

I got it... It came out to be that the Carnot engine can never be 1 and the ones i had before

Thank you for your help... I know it's been a bit frustrating
Thank you

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