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A carnot engine absorbs $2000 J$ of heat from the source of heat engine at $227^{0} C$ and rejects $1200 j$ of heat during each cycle to sink, the temperature of sink and workdone during each cycle is

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$27^{0} C, 800 J$

$300^{0} C, 800 J$

$40^{0} C, 480 J$

$27^{0} C, 480 J$

answer is A.

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Detailed Solution

$n = 1 - \frac{Q_{2}}{Q_{1}} = 1 - \frac{1200}{2000} = 1 - \frac{3}{5} = \frac{2}{5} = 0.4$

$n = 1 - \frac{T_{2}}{T_{1}} 0.4 = 1 - \frac{T_{2}}{227 + 273} 0.6 = \frac{T_{2}}{500} T_{2} = 300 K = 27^{0} C$

$n = \frac{w}{Q_{1}} \Rightarrow 0.4 = \frac{w}{2000} \Rightarrow w = 800 J$

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