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An ideal gas heat engine operates in Carnot cycle between $227^\circ C$ and $127^\circ C$. It absorbs $6 \times 10^{4}$ cals of heat at higher temperature. Amount of heat converted to work is :-
A
$4.8 \times 10^{4}$ cals
B
$2.4 \times 10^{4}$ cals
C
$1.2 \times 10^{4}$ cals
D
$6 \times 10^{4}$ cals
Detailed Solution
$T_1 = 227 + 273 = 500$ K (source) and $T_2 = 127 + 273 = 400$ K (sink)
Efficiency: $\eta = \dfrac{W}{Q_1} = 1 - \dfrac{T_2}{T_1}$
$\eta = 1 - \dfrac{400}{500} = 0.2$
$W = Q_1\left(1 - \dfrac{T_2}{T_1}\right) = 6 \times 10^{4} \times 0.2$
$W = 1.2 \times 10^{4}$ cals
Efficiency: $\eta = \dfrac{W}{Q_1} = 1 - \dfrac{T_2}{T_1}$
$\eta = 1 - \dfrac{400}{500} = 0.2$
$W = Q_1\left(1 - \dfrac{T_2}{T_1}\right) = 6 \times 10^{4} \times 0.2$
$W = 1.2 \times 10^{4}$ cals