JEE Main · 2012 · 29 Apr 2012 · Offline · Heat & Thermodynamics

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A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be

(A)efficiency of Carnot engine cannot be made larger than 50%
(B)1200 K
(C)750 K✓ Correct
(D)600 K

Answer: (C)

Solution

A Carnot engine has efficiency

η = 1 - \frac{T _{sink}}{T _{source}}

. From the first engine,

0.40 = 1 - \frac{T _{sink}}{500}

, so

T_{sink} = 300

K. Keeping that same sink and demanding

η = 0.60

0.60 = 1 - \frac{300}{T}

gives

\frac{300}{T} = 0.40

, so the new source temperature must be

T = \frac{300}{0.40} = 750

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

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