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texas_better
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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.
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.
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)
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.
Homework Statement
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.
Homework Equations
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)
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.