# How Much Heat Is Absorbed/Rejected By The Heat Engine?

If a heat engine undergoes a reversible cycle consisting of two isobaric processes and two adiabatic processes, what methodology is used to determine how much heat is absorbed or rejected by the heat engine in the cycle?

I know that in a carnot cycle, heat is absorbed from a higher temperature bath and rejected to the lower temperature bath, but I am lost on how this is represented mathematically.

• What is your assessment of this so far? Have you at least tried setting up the equations for an isobaric reversible expansion of an ideal gas to see how the temperature and volume change during such an expansion, and to see how much heat must be supplied to the gas? – Chet Miller Mar 19 '18 at 12:17

See if you go through the standard derivation for Carnot's cycle's efficiency philosophy will be clear. Now the other way can be to see through the P-V diagram. For the adiabatic parts $dQ=0$. So only left is an isobaric process. For them heat absorbed will be $P(V_2-V_1)$ considering no change in internal energy also (isothermal).