JEE Main · 2005 · 08 May 2005 · Offline · Heat & Thermodynamics

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

(A) $1/2$
(B) $1/4$
(C) $1/3$ ✓ Correct
(D) $2/3$

Answer: (C)

Solution

Efficiency is the work done in the cycle divided by the heat absorbed. On the temperature-entropy diagram the work equals the area enclosed by the cycle,

\frac{1}{2} S_{0} T_{0}

, while the heat taken in during the stage where both

T

and

S

increase is the area under that line,

\frac{3}{2} S_{0} T_{0}

. So

η = \frac{\frac{1}{2} S _{0} T _{0}}{\frac{3}{2} S _{0} T _{0}} = \frac{1}{3}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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