Thermodynamic Process that Produces the Most Work

In summary, the question asks which compression process requires the most work to reach a final volume given a starting pressure and volume. There is ambiguity in the problem statement as it does not specify if the work is being done by the gas or on the gas by the environment. Depending on the interpretation, the correct answer could be adiabatic or isobaric. However, based on the relevant equation, it can be argued that the isobaric process requires the most work as it has a larger area under the curve, assuming the curves start at the same volume and pressure.
  • #1
sd17
4
6
Homework Statement
Do you think my lecturer is correct in saying this is the correct answer? Question: For a given starting pressure and volume, which of the following compression processes requires the most work to reach a final volume: Isothermal, isobaric, adiabatic, isochoric?
Relevant Equations
delta(U) = Q - W
Screen Shot 2022-06-08 at 4.24.51 PM.png
 
  • Like
Likes Delta2
Physics news on Phys.org
  • #2
You have just posted the model answer. In the homework sections you are required to provide your own arguments and reasoning. So you seem to disagree with the model answer, why?
 
  • #3
Orodruin said:
You have just posted the model answer. In the homework sections you are required to provide your own arguments and reasoning. So you seem to disagree with the model answer, why?
The reason I chose isobaric is because of the diagrams that I have seen in textbooks and other sources where it appears that the area under the curve is greater than other processes.
pvdiagram.jpg
 
  • Wow
Likes Delta2
  • #4
sd17 said:
The reason I chose isobaric is because of the diagrams that I have seen in textbooks and other sources where it appears that the area under the curve is greater than other processes.
The question is about compression, you might want to draw that diagram again, where all the processes start out at the same volume and pressure, and the volume decreases, while the pressure increases.
 
  • Like
Likes Lnewqban, BvU, Delta2 and 1 other person
  • #5
To build a bit upon that. In the diagram you have attached, if you consider the curves curves for compressions (i.e., going right to left along the curves), then they all end at the same volume and pressure. However, the problem statement tells you that the processes should all start at the same volume and pressure, which makes the analysis different.

It is however questionable that the problem statement calls an isochoric process a compression process since volume is constant in such a process by definition.
 
  • Like
Likes Lnewqban
  • #6
willem2 said:
The question is about compression, you might want to draw that diagram again, where all the processes start out at the same volume and pressure, and the volume decreases, while the pressure increases.
Thank you for your input I am now able to see that adiabatic is the correct answer.
 
  • Like
Likes vela, Lnewqban and Delta2
  • #7
Orodruin said:
To build a bit upon that. In the diagram you have attached, if you consider the curves curves for compressions (i.e., going right to left along the curves), then they all end at the same volume and pressure. However, the problem statement tells you that the processes should all start at the same volume and pressure, which makes the analysis different.

It is however questionable that the problem statement calls an isochoric process a compression process since volume is constant in such a process by definition.
Thank you for your reply I am now able to understand the reasoning behind the correct answer.
 
  • Like
Likes Lnewqban
  • #8
sd17 said:
Homework Statement:: Do you think my lecturer is correct in saying this is the correct answer? Question: For a given starting pressure and volume, which of the following compression processes requires the most work to reach a final volume: Isothermal, isobaric, adiabatic, isochoric?
Relevant Equations:: delta(U) = Q - W
Am I the only one to think that the statement of the problem is ambiguous? I am always wary when I see "work" mentioned without reference as to who is doing the work on whom. Prepositions are particularly important in this case. If we compare the isobaric and adiabatic processes, the magnitude of the work done is positive regardless of whether the work is done by the gas or on the gas by the environment. The isobaric process has more area under the curve which makes the magnitude of the work (amount of Joules) exchanged with the environment greater than the adiabatic.

For a compression, the work done by the gas on the environment is always negative. A negative number with a larger magnitude is smaller, so the answer would be "adiabatic" because it is closer to zero than "isobaric". However, the reverse would be true for the work done on the gas by the environment and the correct answer would be "isobaric". Does "most" work in the statement of the problem mean "more Joules exchanged" or does it mean "the larger of two negative numbers"?

In my mind, the question is ambiguous because of the lack of prepositions. The only clue that we have is OP's relevant equation of the first law. One can tell by the negative sign that ##W## is the work done by the gas on the environment. However, many textbooks write the first law with a plus sign in front of ##W## which implicitly defines it as the work done on the gas by the environment. I think that in this case, the proper use of prepositions would have made the correct answer independent of which convention one uses for the first law.
 
  • #9
kuruman said:
The isobaric process has more area under the curve
No it does not. Not if drawn in accordance with the problem statement that specifies equal pressure and volume before compression, ie, the curves should coincide on the right side. The isobaric curve will lie below all the others.
 
  • Like
Likes Delta2
  • #10
Orodruin said:
No it does not. Not if drawn in accordance with the problem statement that specifies equal pressure and volume before compression, ie, the curves should coincide on the right side. The isobaric curve will lie below all the others.
Yes, of course. I should have drawn an actual diagram instead of doing it in my head. Anyway, I had my rant for the day.
 
  • Like
Likes Delta2

1. What is a thermodynamic process?

A thermodynamic process is a series of changes in a thermodynamic system that involves the transfer of energy and can result in work being done.

2. What is the most efficient thermodynamic process for producing work?

The most efficient thermodynamic process for producing work is the Carnot cycle, which involves a reversible process between two heat reservoirs.

3. How does the thermodynamic process that produces the most work work?

The thermodynamic process that produces the most work works by converting heat energy into mechanical work through a series of processes, such as expansion and compression of a gas.

4. What factors affect the efficiency of a thermodynamic process?

The efficiency of a thermodynamic process is affected by factors such as temperature, pressure, and the type of working fluid used.

5. How is the efficiency of a thermodynamic process calculated?

The efficiency of a thermodynamic process is calculated by dividing the work output by the heat input. This is known as the Carnot efficiency and is represented by the equation: efficiency = (T1-T2)/T1, where T1 is the temperature of the heat source and T2 is the temperature of the heat sink.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
949
  • Introductory Physics Homework Help
Replies
5
Views
744
  • Introductory Physics Homework Help
Replies
1
Views
144
  • Introductory Physics Homework Help
Replies
1
Views
888
  • Introductory Physics Homework Help
Replies
19
Views
1K
  • Introductory Physics Homework Help
Replies
18
Views
746
  • Introductory Physics Homework Help
Replies
30
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
179
  • Introductory Physics Homework Help
Replies
3
Views
941
Back
Top