Understanding PV Diagrams: Analyzing Work, Heat, and Temperature Changes

[lc99]

Homework Statement

Homework Equations

The Attempt at a Solution

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I was wondering if the answer is all statements are true. I want to know if my reasons are correct:

1) the work done by the system is greatest along path 1 because work done is equal to the area under the path. The path under 1 is clearly largest of the two other paths.

2) if Ub > Ua , then Q is greatest along path b. Since the delta U for the other paths are equal to that of path 1, the equation becomes Q=W for all paths as delta U can be ignored in comparison. Q is largest for path 1 because W is largest.

3)Heat is absorbed by the system because Q is positive since deltaU is positive. When Q is positive, this means that heat is added to the system (same as heat aborbed by the system).

 

[TSny]

It all looks good to me except for the first part of your statement 2 where you said

2) if Ub > Ua , then Q is greatest along path b.

There is no path b. But the rest of your statement 2 appears to be correct. You are right that ΔU is the same for all paths, so you don't need to worry about ΔU when comparing paths for Q. But, still, I wouldn't write Q = W.

 

[lc99]

It all looks good to me except for the first part of your statement 2 where you said
There is no path b. But the rest of your statement 2 is right. Also, you are right that ΔU is the same for all paths, so you don't need to worry about ΔU when comparing paths for Q. But, still, I wouldn't write Q = W.

oops , you are right. i meant path 1. Also, I guess it was easier to understand it if i wrote Q=W.

Also, regardless of statement 2, it's true that change in U is the same for all of them, but I am unsure if change is U increases? I would think U increases. Is there any information that would say so?

 

[TSny]

Also, regardless of statement 2, it's true that change in U is the same for all of them, but I am unsure if change is U increases? I would think U increases. Is there any information that would say so?

Consider the product PV for the initial and final states. Which state has the higher value for PV? What does that tell you about the temperatures for the initial and final states? For an ideal gas, how is U related to temperature?

 

[lc99]

Consider the product PV for the initial and final states. Which state has the higher value for PV? What does that tell you about the temperatures for the initial and final states? For an ideal gas, how is U related to temperature?

Ahh. That makes sense. U is higher in the final state because of the temperature increase due to PV relationship.

Also, is it also correct to say that temperature increases because isotherms tend to be up and into the graph which represent higher temperatures?

 

[TSny]

Also, is it also correct to say that temperature increases because isotherms tend to be up and into the graph which represent higher temperatures?

Yes.