Understanding Isothermal Work: Solving the Gas Compression Problem

[ChiralSuperfields]

Homework Statement

please see below

Relevant Equations

PV = nRT

For this problem,

dose anybody please give me guidance how they got 74 K as the answer? Note that chat GPT dose not give the correct answer (it gives the temperature of the gas is 1500 K).

Many Thanks!

 

[kuruman]

This is a homework problem. You know the rules. Please show some work. I would also suggest that you look at the chat GPT answer and see whether there is anything you can use.

 

[ChiralSuperfields]

This is a homework problem. You know the rules. Please show some work. I would also suggest that you look at the chat GPT answer and see whether there is anything you can use.

Thank you for your reply @kuruman!

Since this is an ideal gas, I though I could you the ideal gas law. So as far as I got was setting the temperatures equal $\frac{P_iV_i}{nR} = \frac{P_fV_i}{5nR}$ which gave $5P_i = P_f$.

Many thanks!

 

[TSny]

If you use calculus in your course, then your professor or textbook has probably derived a formula for the work associated with a quasi-static, isothermal expansion/compression of an ideal gas.

 

[ChiralSuperfields]

If you use calculus in your course, then your professor or textbook has probably derived a formula for the work associated with a quasi-static, isothermal expansion/compression of an ideal gas.

Thank you for your reply @TSny!

No sorry, this course is algebras based. We did not do the calculus parts and alot of the thermo so stuff it not really making sense very much.

Many thanks!

 

[ChiralSuperfields]

If you use calculus in your course, then your professor or textbook has probably derived a formula for the work associated with a quasi-static, isothermal expansion/compression of an ideal gas.

Its an intro physics course so we cover dimensional analysis then thermo, and eventually mechanics and waves.

 

[ChiralSuperfields]

Nevermind, I think I really overthought this simple problem. Sorry.

 

[TSny]

Its an intro physics course so we cover dimensional analysis then thermo, and eventually mechanics and waves.

Ok. I wonder if the formula for isothermal work was given to you without a derivation. I don't see how to work the problem without this formula.

 

[ChiralSuperfields]

Ok. I wonder if the formula for isothermal work was given to you without a derivation. I don't see how to work the problem without this formula.

Thank you for your reply @TSny! Yeah, the only way I now realize that this problem to be solved is if we assume pressure it not constant, which then I have to use the work integral in terms of differential volume which was not shown in class. We were only shown $W = P(V_2 - V_1)$ which I now know assumes the special case where the pressure is constant.