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About the 2nd Carnot Corollary

Physics Asked by Raihan on April 21, 2021

I have a question about the 2nd Carnot Corollary.

According to Moran, Fundamentals of Engineering Thermodynamics, the 2nd Carnot Corollary stated that “all reversible power cycles operating between the same two thermal reservoirs have the same thermal efficiency.”

However, later in some examples on Vapor Power System and Gas Power System, the efficiency of ideal Rankine cycle and ideal Brayton cycle are lower than that of Carnot cycle.

I am confused because this fact is contradicting with the 2nd Carnot Corollary. Can someone please explain me where did I understand wrong?

Thank you 🙂

2 Answers

Because the Rankine cycle does not operates between two reservoirs (that is , one of the steps involves heat absorption during a change in temperature). Same with the Brayton cycle.

Answered by user167013 on April 21, 2021

A Carnot cycle is always defined as one that has 4 reversible stages (1) isothermal heat absorption from a thermostat at temperature (heat source) $T_{high}$, (2) adiabatic work absoprtion (compression) from a work source, (3) isothermal heat release into a thermostat (heat sink) at $T_{low}$, (4) adiabatic work release (exapansion) in to a work sink. The reversible Carnot cycle's efficiency is always $1 - frac {T_{low}}{T_{high}}$. A reversible adiabatic process is isentropic.

In the Rankine cycle, the work stages (2) and (4) are nearly but not exactly isentropic, hence slightly irreversible. Stage (3) is essentially isothermal as it involves a phase transition from steam to liquid water. Stage (1) that starts with liquid water and ends with steam is not isothermal, it is in fact isobaric, and it is only during the water's phase transition is isothermal, not in the beginning nor towards the end. The Rankine cycle is not a Carnot cycle unlike the Brayton cycle that is in fact a Carnot cycle. See the diagrams on https://en.wikipedia.org/wiki/Brayton_cycle and https://en.wikipedia.org/wiki/Rankine_cycle

Answered by hyportnex on April 21, 2021

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