Why Do Different Methods Yield Different Efficiencies in a Reversible Cycle?

[L0r3n20]

I just read about Carnot theorem (the highest efficiency is the one of reversible machines and all reversible machines working between two given temperatures have the same efficiency).

Then I found a problem where I have a reversible cycle made of an isochoric, adiabatic and isotherm. I report here the data. Computing the efficiency as work/absorbed heat I get 0.12 while if I use 1-Tc/Th I have 0.25. Why are the twos not the same?

The problem states:
"A monoatomic ideal gas is in a state A where the temperature is 300K, p= 2atm and V = 20L. Through an isochoric process the temperature rise up to 400K (state B); through an adiabatic process the gas arrive in a state C where Tc = Ta = 300K and finally through an isotherm process it gets back to A. Compute the efficiency of the cycle.

 

[TSny]

Good question. When people say that "all reversible engines working between two given temperatures have the same efficiency", they are talking about cases where heat is transferred to or from the engine only at the two given temperatures. In the example with the isochoric process, the temperature of the engine will continuously increase as heat is added during the isochoric process. So, the engine will take in heat at temperatures intermediate between the two given temperatures. This cycle has less efficiency compared to a cycle where all of the heat is added at the highest given temperature.

 

[L0r3n20]

Thanks! That's exactly what I needed To understand!