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Work & Final Temperature in Piston Cylinder (Check my work)
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Oct13-12, 09:05 AM
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 [itex]V = vm[/itex]. 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)
-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.
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