Question

A Carnot heat engine absorbs heat from three thermal reservoirs at 1000 K, 800 K and 600 K. The engine develops 10 kW of power and rejects 6.67 kW of heat to a sink at 300 K. If the heat supplied by reservoir at 1000 K is 60% of the heat supplied by a resevoir at 600 K, then the heat supplied by the reservoir at 800 K is closest to

• A. 500 kJ/min
• B. 310 kJ/min
• C. 550 kJ/min
• D. 410 kJ/min

Answer 1

The correct option is A 500 kJ/min


From clausius inequality for a reversible heat engine :

$\oint \frac{\delta Q}{T}=0$

$\Rightarrow \frac{0.6Q_1}{1000}+\frac{Q_2}{800}+\frac{Q_1}{600}-\frac{6.67}{300}=\mathrm{0....}\left(i\right)$

Also by energy balance :

$0.6Q_1+Q_2+Q_1-6.67=\mathrm{10....}\left(ii\right)$
From (i) and (ii)
$Q_2=500kJ/min$