- #1

ForgetfulPhysicist

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- Homework Statement
- Heat Engine with working substance characterized by energy E = g T^a V, with a>1 and g>0 being known coeﬃcients. The values of P1, V1 are also known. Find P2 /P1 in terms of the known quantities.

- Relevant Equations
- dE = TdS - PdV

My attempted solution is as follows:

Obviously the heat transfer happens during transitions 1->2 and 3->1.

It's also clear that

P1 = P3

V1 = V2

E2 - E1 = Integral[T dQ , from state 1 to state 2]

E3 - E2 = - Integral[P dV , from state 2 to state 3]

E1 - E3 = Integral[T dQ , from state 3 to state 1] + 7 P1 V1

But I can't find a way to perform any of these integrals or make any progress on this problem.

An attempt to calculate pressure is stuck at: p = - (dE/dV)_S = g a T^(a-1) (dT/dV)_S V + g T^a

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