Determine the work done by the gas

[yossup]

Homework Statement

A 1.10 mol sample of an ideal diatomic gas at a pressure of 1.20 atm and temperature of 420K undergoes a process in which its pressure increases linearly with temperature. The final temperature and pressure are 720K and 1.83atm.

Determine the work done by the gas.

Determine the heat added to the gas.

Homework Equations

E= 5/2 nRT

The Attempt at a Solution

So the change in internal energy I calculated to be 6860J.

So W + Q = 6860.

I can't figure out how to calculate W or Q because I don't know what kind of process this is (adiabatic, isobaric, isochoric, etc.) It just says pressure increases linearly with temperature. :(

 

[Ygggdrasil]

Think of the ideal gas equation. If pressure increases linearly with temperature, what does that tell you about the process.

 

[yossup]

isochoric! :D

 

[Ygggdrasil]

Exactly. That make's the subsequent calculations really easy :)

 

[yossup]

if it's isochoric, the work done by the gas should be zero but it says I'm wrong so it isn't isochoric?

 

[Ygggdrasil]

Something's wrong with the problem. It says P increases linearly with T, but P_1/T_1 is not equal to P_2/T_2.

 

[yossup]

isn't that because it's not at constant volume?

P1/T1 = P2/T2 only at constant volume... :(

 

[Ygggdrasil]

But if P increases linearly with T then P = c T, where c is a constant, so P/T = c implying that P_1/T_1 = P_2/T_2