First slide

Heat Engine; Carnot Engine and refrigerator

Question

A carnot engine working between 300 K and 600 K has a work output of 800 J per cycle, the amount of heat energy supplied to the engine from the source in each cycle is

Moderate

A

800 J
B

3200 J
C

1600 J
D

6400 J

Solution

$\begin{array}{rcl} efficiency of carnot engine is η=1- \frac{T_{2}}{T_{1}} \\ h e r e T_{1} =source temperature(hot)=600K (given) \\ T_{2} =sink temperature(cold)=300K (given) \\ s u b s t i t u t e i n e f f i c i e n c y e q u a t i o n \\ η =1- \frac{300}{600} \\ \Rightarrow & η = 1 - \frac{1}{2} \\ \Rightarrow & η = \frac{1}{2} \\ a m o u n t o f h e a t e n e r g y s u p p l i e d t o e n g i n e i s Q=? \\ η = \frac{Work done(W)}{Heat given(Q)} \\ s u b s t i t u t e v a l u e o f η, a n d g i v e n W & = & 800 J \\ \Rightarrow & \frac{1}{2} = \frac{800}{Q} \\ Q=1600 J \end{array}$

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