(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 1.20 mol sample of an ideal diatomic gas at a pressure of 1.20 atm (P_{1}) and temperature of 380 K (T_{1}) undergoes a process in which its pressure increases linearly with temperature. The final temperature and pressure are 680 K (T_{2}) and 1.83 atm (P_{2}).

(b) Determine the work done by the gas.

2. Relevant equations

(T_{2}- T_{1}) / (P_{2}- P_{1}) = constant

V_{2}/ V_{1}= P_{1}T_{2}/ P_{2}T_{1}

PV = nRT

W = integral of PV

3. The attempt at a solution

The answer is supposed to be [nR(P_{1}T_{2}- P_{2}T_{1}) ln(P_{2}/P_{1})] / (P_{2}- P_{1})

but I can't figure out how to get there despite the hours I have poured into this problem. All I know is that volume is not constant in order for there to be work done. Also, I have the vague idea of finding the linear equation or relationship between T and P using that equation to plug in T in PV = nRT. Then, technically, there would be a graph for PV and I could solve for V_{1}and V_{2}, which can be the limits of integration for the integral of PV (to get work). But isn't that way too complicated, especially as an integral...so I was wondering whether someone else has any idea.

Please help explain, and thank you!

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# Physics Thermodynamics - Finding Work

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