Question

III. A Carnot heat engine operates between a source at 1000 K and a sink at 300 K. If the heat engine is supplied with heat at a rate of 800 kJ/min, determine (a) the thermal efficiency and (b) the power output of this heat engine\

Answer 1

Answer:

70 %

9.33331 kW

Explanation:

Q = Heat supplied = 800 kJ/min

$T_h$ = Hot reservoir = 1000 K

$T_c$ = Cold reservoir = 300 K

Converting kJ/min to kW

$800\times \frac{1}{60}=13.3333\ kW$

Thermal efficiency

$\eta=1-\frac{T_c}{T_h}\\\Rightarrow \eta=1-\frac{300}{1000}\\\Rightarrow \eta=0.7$

The thermal efficiency is 70%

Efficiency

$\eta=\frac{W}{Q}\\\Rightarrow W=\eta Q\\\Rightarrow W=0.7\times 13.3333\\\Rightarrow W=9.33331\ kW$

The power output of the engine is 9.33331 kW