Pressure change with constant volume

[SadStudent]

Homework Statement

Given two moles of some gas with two atoms per molecule which has energy U=aK_{B}T.
Assume the initial pressure is P_{i}= 2 Atm and the initial volume is P_{i}= 0.001\ m^{3}.
Now we heat it in an isochoric process to 2P_{i}.

What would be \Delta T?
What would be the work required to do that?
What would be the change in the gas particles' internal energy?

Homework Equations

U=aK_{B}T
dU=PdS-TdV

The Attempt at a Solution

Well using the first law of thermodynamics, I got that under constant volume dV=0 so \frac{dQ}{dT}=\frac{\partial U}{\partial T} so the entire energy that we spent on heating would be transferred into the gas.
What's a tricky to me is to formulate the change in temperature as a function of pressure because dV=0 so I'd really welcome a hint.

Thanks!

 

[TSny]

Homework Equations

dU=PdS-TdV

Oops, check that.

What's a tricky to me is to formulate the change in temperature as a function of pressure because dV=0 so I'd really welcome a hint.

Can you assume the gas obeys the ideal gas law?

 

[SadStudent]

Oops, check that.Can you assume the gas obeys the ideal gas law?

And yes of course it was a typo :) it's supposed to be dU=TdS-PdV

I'm really not sure whether I can, is there a way of solving this without this assumption?