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  4. A Carnot's cycle operating between T1= 600 K and T2 = 300 K producing 1.5 kJ of mechanical work per cycle. The heat transferred to the engine by the reservoirs is

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Q. A Carnot's cycle operating between $T_1= 600\, K$ and $T_2 = 300 \,K$ producing $1.5 \,kJ $ of mechanical work per cycle. The heat transferred to the engine by the reservoirs is

Thermodynamics

Solution:

Here, $T_{1} = 600 \,K, $
$T_{2}= 300\, K, $
$W = 1.5k \,J = 1500 \,J,$
As $\eta = 1 -\frac{T_{2}}{T_{1}} = 1 -\frac{300}{600} = \frac{1}{2} $
Also, $\eta= \frac{\text{work done }}{\text{heat supplied}} = \frac{W}{Q_{1}} $
$\therefore Q_{1} = \frac{W}{\eta} = \frac{1500}{1/2 }$
$= 3000\,J = 3\,kJ$