Homework Help: Work & Final Temperature in Piston Cylinder (Check my work)

1. Oct 13, 2012

texas_better

If someone or a few people, just look this over and tell me if I'm right or if I did something wrong I'd be so grateful. I think it's all there but I'm not sure, there might be something off.

1. The problem statement, all variables and given/known data

Air (which behaves like an ideal gas) undergoes adiabatic expansion in piston cylinder.
T1 = 2000 K
p1 = 4 MPa

Undergoes adiabatic expansion to a volume that is v2 = 10v1. (v = specific vol)

Find T2 (temperature of gas after expansion) and calculate adiabatic work, W, done.

2. Relevant equations

3. The attempt at a solution

I found W = 863 kJ and I know this correct.

The way I did it was by solving for v, specific volume, in pv = RT, and then putting V, volume, in terms of v and m, mass, like $V = vm$. I then used the polytropic process and the V1's cancel when you sub V2=10V1. I end up w/ 863m (kJ).

Then used Q - W = E2-E1.
Q is 0 (adiabatic)
Then,
-W = E2-E1
-W = U2-U1 only internal energy
-W = m(u2-u1) where u = specific enthalpy
-W = mcv(u2-u1) where cv=0.718 kJ/kg*k for air
-W = mcv(T2-T1)

In the final step I substituted W = 863m (kJ), the cv value, T1 = 2000 K, and solved for T2 to get 797k.

Is this legit? Thanks for any help.