- 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