First slide

Heat engine

Question

An ideal gas heat engine operates in a Carnot's cycle between $227^{0} C and 127^{0} C$ . It absorbs $6 x {lO}^{4}$ J at high temperature. The amount of heat converted into work is ....

Moderate

A

$4.8 \times 10^{4} J$
B

$3.5 \times 10^{4} J$
C

$1.6 \times 10^{4} J$
D

$1.2 \times 10^{4} J$

Solution

$η = 1 - \frac{T_{2}}{T_{1}} = 1 - \frac{400}{500} = \frac{1}{5} ∴ η = \frac{W}{Q}$
$\Rightarrow \frac{1}{5} = \frac{W}{Q}$
$\Rightarrow W = \frac{Q}{5} = \frac{6}{5} \times 10^{4} = 1.2 \times 10^{4} J$

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