Question

The temperature of the working fluid in a real heat engine cycle changes during heat addition and heat rejection processes. The maximum and minimum temperatures of the cycle are $T_{\max}$ and $T_{\min}$, respectively. If $\eta_C$ is the thermal efficiency of a Carnot engine operating between these temperature limits, then the thermal efficiency, $\eta$, of the real heat engine satisfies the relation

• A. $\eta>\eta_C$
• B. $\eta<\eta_C$
• C. $\eta = \eta_C$
• D. $\eta = 1 + \eta_C$

Hint:

Carnot efficiency is the theoretical upper limit for any engine between two temperatures. Real engines always have lower efficiency due to unavoidable irreversibilities.

Answer 1

The Correct Option is B

A Carnot engine represents the \textit{maximum possible efficiency} for any heat engine operating between two temperature limits $T_{\max}$ and $T_{\min}$. It is an ideal, reversible engine with no irreversibilities or losses. Real heat engines, however, always experience friction, heat losses, finite temperature differences, and other irreversibilities.
Thus, a real engine must always have lower efficiency compared to the Carnot efficiency:
\[ \eta<\eta_C = 1 - \frac{T_{\min}}{T_{\max}}. \] Since no real engine can exceed or even reach the Carnot efficiency, the only valid relation is:
\[ \boxed{\eta<\eta_C}. \]