Isobaric and Isochoric Process Combined

[RMalt]

Homework Statement

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This is a very basic question. I have a cylinder filled with air having stops at a particular height .
First part of the process is isobaric as piston is free to move and P is constant.
When piston reaches stops this becomes isochoric process as volume is constant.

So far so good...

I need to sketch the T-V, P-V and P-T Diagrams on the same axis.

Homework Equations

Not sure of any equations that will help me in this, just knowledge of how Temperature, pressure and volume effect each other.

The Attempt at a Solution

I have drawn the P-v diagram as shown in the picture below. This is the easiest one to draw of all 3 as Pressure is constant in isobaric while volume is constant in isochoric

I know that in an isobaric process, T and V are directly proportional. I cannot find any information about T-V diagram from isochoric process and how these should be put together.

Also, I know that in an isochoric Process P and T are directly proportional. However I cannot understand how the P-T diagram for isobaric process will look like.

Unknown: T-V ---> isochoric and how this will look like when an isobaric process is added. (Check second picture for uploaded T-V diagram.
P-T ---> isobaric and how this will look when an isochoric process is added.

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[zexxa]

Are you sure your P-V diagram is correct? Isn't the order of events an isobaric expansion -> isochoric expansion? This looks like isochoric -> isobaric if I go from left to right that is.

If you want to draw the P-T and T-V diagram, you just need 1 simple equation that I'm pretty sure you have been using before you reached this stage.

 

[RMalt]

I know that general gas law can be applied in this case, and also:
Boyle's Law: PV = k
Gay-Lussac's Law: P/T =k
Charles Law: V/T =k

However for the T-V diagram of an isochoric process this cannot be done by applying the above laws, or can it ? Since temperature may vary while volume remains constant. The same for the P-T diagram of an isobaric process.

 

[zexxa]

Yes these equations can help to explain how temperature varies with the changes.
However you can also look at the isotherms to determine their change over the processes too.
Gay-Lussac's and Charles' laws are more than sufficient to see that they P-T and V-T are linearly correlated.

So to determine how well they are related, just take the differential with to the proper axis and you'll be able to draw the graph.

By the way, I pointed out that your PV diagram above is incorrectly ordered.

 

[RMalt]

Thanks for your time on this matter. I will see what I can manage.

 

[zexxa]

You're welcome :)

 

[RMalt]

Hi again, I am starting to think that my diagram i drew is correct. That is because the isobaric process starts at point 1 however as this process is ongoing, the volume is decreasing. So the isochoric process starts at a lesser volume than the initial.

If it was drawn the other way it would mean that during the isobaric process, volume actually increased which is not true.

 

[RMalt]

Attached are my diagram drawings. DO you agree? What improvements can be made?

 

[zexxa]

Sorry for the late reply,

Your graphs are consistent with each other. However I guess the disagreement I had with you at the start could be due to the wordings you presented your question as. You said that you had an air filled cylinder and the piston is free to move, I assumed that the piston was moving to expand the volume the air can take as this is the usual case in concept questions. I suppose you meant that the air was being extracted out and the free piston is following the compression process.