Question

Efficiency of an engine is 0.4 , when temperature of its sink (cold body ) is
300K .What is the temperature of the hot body? Find its efficiency ,if the
temperature of the hot body is kept unchanged , while temperature of the sink
is lowered by 50K .(treat it as reversible engine)

Answer 1

Answer:

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Answer 2

The efficiency of a heat engine is given by,

$\longrightarrow\sf{\eta=1-\dfrac{T_2}{T_1}}$

where $\sf{T_1}$ and $\sf{T_2}$ are temperatures of source and sink respectively.

According to the question, the efficiency is 0.4 when temperature of sink is 300 K.

$\longrightarrow\sf{0.4=1-\dfrac{300}{T_1}}$

$\longrightarrow\sf{T_1-300=0.4T_1}$

$\longrightarrow\sf{0.6T_1=300}$

$\longrightarrow\sf{T_1=500\ K}$

That is, temperature of source is 500 K.

So the efficiency of the engine when temperature of sink is lowered by 50 K keeping temperature of source unchanged is,

$\longrightarrow\sf{\eta'=1-\dfrac{300-50}{500}}$

$\longrightarrow\sf{\eta'=1-\dfrac{250}{500}}$

$\longrightarrow\sf{\underline{\underline{\eta'=0.5}}}$

Hence new efficiency is $\bf{0.5.}$