Piston/cylinder expands polytropically

[OsDaJu]

Homework Statement

A piston/cylinder contains helium at 500 K and 1200 kPa. It expands polytropically with n=1.667 to a pressure of 100 kPa. Find the final temperature, the specific work and specific heat transfer in the process

Homework Equations

U2-U1=1Q2-1W2
1W2=P2V2-P1V1/(1-n)
P1*V1^n=P2*V2^n
PV=mRT

The Attempt at a Solution

(P1V1/T1)=mR=(P2V2/T2)

I'm trying to plug that into this equation (P1*V1^n=P2*V2^n) to find P or T but I can't since I don't have enough data to use it.

I only have intensive information to work with. Can I assume that this is an ideal gas or should I look for the stage it is in? What am I doing wrong?

 

[rock.freak667]

$$\frac{P_1 V_1}{T_1}=\frac{P_2 V_2}{T_2}$$


make V₁ the subject and then sub that into P₁V₁ⁿ=P₂V₂ⁿ

You should then get an equation involving P₁,P₂,T₁,T₂ and n