Change in entropy for adiabatic compression

[Bugsy23]

Homework Statement

A sample of 8.02*10^-1 moles of nitrogen gas ($$\gamma$$=1.4) occupies a volume of 2*10^-2m^3 at pressure 1*10^5pa and temperature 300K. The gas is adiabatically compressed to half its original volume. What is the change in entropy of the gas?

Homework Equations

S2-S1=C_vIn(P2/P1)+C_pIn(V2/V1)

PV=nRT

The Attempt at a Solution

I have already worked out the values for C_v and C_p and the change in volume of the gas, but I don't know how to find the change in pressure. Since nitrogen behaves as an ideal gas, it should be possible to find it using PV=nRT, but that also requires knowing the change in temperature. Is there a different way of working out the change in pressure?

 

[Andrew Mason]

You have to use the adiabatic condition. This condition shows the relationship between P and V in an adiabatic change. Hint: it uses $\gamma$

AM