A Carnot's engine working between $400 K$ and $800 K$ has a work output of $1200 J$ per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :

$1800 J$

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$3200 J$

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$2400 J$

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$1600 J$

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Solution

The correct option is C
$2400 J$

Step 1. Given data
Temperature, $T_{1} = 800 K$
Temperature, $T_{2} = 400 K$
Work done, $W = 1200 J$
Step 2. Finding the Efficiency, $η$
By using the formula of Efficiency
$η = 1 - \frac{T_{2}}{T_{1}}$
$η = 1 - \frac{400}{800}$
$η = \frac{1}{2}$
Step 3. Finding the amount of heat supplied, $Q$
By using the formula, $η = \frac{W}{Q_{}}$
$\frac{1}{2} = \frac{1200}{Q}$
$Q = 2400 J$
Therefore, the amount of the heat supplied is $2400 J$
Hence, the correct option is C.

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