Thermodynamics: Compression of an Adiabatic Gas

[Minescrushessouls]

Homework Statement

Assume 1.500 mol of a monatomic ideal gas is compressed from 3.00 L to 1.00 L.

a. If the initial and final temperature is 10.0 °C, what are the initial and final pressures (in atm)?

b. How much work input (in kJ) is required if a reversible isothermal path at 10.0 °C is followed?

c. How much work input (in kJ) is required if the compression is adiabatic rather than isothermal? Assume the initial temperature is 10.0 °C.

Homework Equations

PV=nRT
w=-nRTln(vf/vi)
U=q+w

The Attempt at a Solution

I got both a and b using the first two equations I listed. I got the inital pressure to be 11.6 atm and the final pressure to be 34.8 atm. For the second part I got the work to be 3.88 kJ.

I'm stuck on the third part. I know adiabatic means that there no change in U, so q=-w but I don't know how that applies to the question.

 

[DrClaude]

You're missing an equation for the energy U of an ideal gas. And adiabatic does not mean ΔU = 0, it means q = 0.

 

[Minescrushessouls]

So ΔU=-PΔV, where U=w

But the problem isn't isobaric, so that equation wouldn't work. I can't seem to find another equation though...