Ncert Exercises & Solutions

Consider a Carnot’s cycle operating between $T_{1}$ $T_{1}$ = 500 K and $T_{2}$ $T_{2}$ = 300 k producing 1 kJ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.

Hint: The work produced per unit heat transferred will be equal to the efficiency of the engine.

Step 1: Find the efficiency of the engine.

Given, the temperature of the source,

T_{1}

$T_{1}$ = 500K

The temperature of the sink,

T_{2}

$T_{2}$ = 300K
Work cone per cycle, W = 1k J= 1000 J
Heat transferred to the engine per cycle,

Q_{1}

$Q_{1}$ =?The efficiency of a Carnot engine,

(η) = 1 - \frac{T_{2}}{T_{1}} = 1 - \frac{300}{500} = \frac{200}{500} = \frac{2}{5}

$(η) = 1 - \frac{T_{2}}{T_{1}} = 1 - \frac{300}{500} = \frac{200}{500} = \frac{2}{5}$

Step 2: Find the heat transferred.

and

η = \frac{W}{Q_{1}}

$η = \frac{W}{Q_{1}}$

\Rightarrow Q_{1} = \frac{W}{η} = \frac{1000}{(2 / 5)} = 2500 J

$\Rightarrow Q_{1} = \frac{W}{η} = \frac{1000}{(2 / 5)} = 2500 J$

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