First slide

Heat engine

Question

A Carnot engine working between 300 K and 600 K has work output of 800 J cycle^-1. The amount of heat energy supplied from the source of engine in each cycle is

Moderate

A

800 J
B

1600 J
C

3200 J
D

6400 J

Solution

The efficiency of Carnot engine is given by
$η = 1 - \frac{T_{2}}{T_{1}}$
Given, $T_{1} = 600 K, T_{2} = 300 K$
$∴ η = 1 - \frac{300}{600}$
$\Rightarrow η = 1 - \frac{1}{2} \Rightarrow η = \frac{1}{2} = 50 %$
Also, $η = \frac{W}{Q} \Rightarrow \frac{800}{Q} = \frac{1}{2}$
Thus, amount of heat supplied from source to engine is
$Q = 800 \times 2 = 1600 J$

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