About the 2nd Carnot Corollary

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 :)

• Do you mean that the efficiency of these engines is less than $1-\frac{T_{cold}^{}}{T_{hot}^{}}$? Are they working in the reversible limit? – Sunyam Oct 13 '17 at 12:31
• Thus for sure the ideal Rankine and Brayton cycles operating between two sources are not reversible. – Diracology Oct 13 '17 at 12:36
• Does the Rankine cycle operate between just two reservoirs, each at fixed temperature? – Philip Wood Oct 13 '17 at 12:39
• Ahh! I see! So you mean that the corollary is true for two reservoirs with fixed temperature, am I right? If it's so, then this makes sense bcs there is a temperature change in T-s diagram for ideal Rankine and Brayton cycle – Raihan Oct 13 '17 at 12:58

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.