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Work & Final Temperature in Piston Cylinder (Check my work) 
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#1
Oct1312, 09:05 AM

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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. 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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