Thermodynamics Ques 45
45. An ideal gas heat engine operates in a Carnot cycle between $227^{\circ} C$ and $127^{\circ} C$. It absorbs $6$ $kcal$ at the higher temperature. The amount of heat (in kcal) converted into work is equal to
[2002]
(a) $1.2$
(b) $4.8$
(c) $3.5$
(d) $1.6$
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Answer:
Correct Answer: 45.(a)
Solution:
- (a) Efficiency $=\frac{T_1-T_2}{T_1}$
$T_1=227+273=500$ $ K$
$T_2=127+273=400 $ $K$
$\eta=\frac{500-400}{500}=\frac{1}{5}$
Hence, output work $=(\eta) \times$ Heat input $=\frac{1}{5} \times 6=1.2 $ $kcal$
Efficiency of heat engine: $n=\frac{\text{ Work done }(W)}{\text{ Heat in put }(Q_1)}$ $=1-\frac{Q_2}{Q_1}=1-\frac{T_2}{T_1}$
BETA
