- #1

misa

- 8

- 0

## Homework Statement

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.

## Homework 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

## 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!**