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.(adsbygoogle = window.adsbygoogle || []).push({});

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

Air (which behaves like an ideal gas) undergoes adiabatic expansion in piston cylinder.

T_{1}= 2000 K

p_{1}= 4 MPa

Undergoes adiabatic expansion to a volume that is v_{2}= 10v_{1}. (v = specific vol)

Find T_{2}(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 V_{1}'s cancel when you sub V_{2}=10V_{1}. I end up w/ 863m (kJ).

Then used Q - W = E_{2}-E_{1}.

Q is 0 (adiabatic)

Then,

-W = E_{2}-E_{1}

-W = U_{2}-U_{1}only internal energy

-W = m(u_{2}-u_{1}) where u = specific enthalpy

-W = mc_{v}(u_{2}-u_{1}) where c_{v}=0.718 kJ/kg*k for air

-W = mc_{v}(T_{2}-T_{1})

In the final step I substituted W = 863m (kJ), the c_{v}value, T_{1}= 2000 K, and solved for T_{2}to get 797k.

Is this legit? Thanks for any help.

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# Work & Final Temperature in Piston Cylinder (Check my work)

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