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  4. A Carnot engine working between 300 K and 400 K has 800 J of useful work. The amount of heat energy supplied to the engine from the source is

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Q. A Carnot engine working between $300\, K$ and $400\, K$ has $800\, J$ of useful work. The amount of heat energy supplied to the engine from the source is

KCETKCET 2016Thermodynamics

Solution:

$\eta =\frac{\text { Work done }}{\text { Heat supplied }}$
$=\frac{T_{1}-T_{2}}{T_{1}}=\frac{W}{Q_{1}} $
$W =800\, J , T_{1}=400\, K , T_{2}=300 \,K$
On substitution the values
$\frac{800}{Q_{1}} =\frac{400-300}{400}$
$=\frac{100}{400}=\frac{1}{4} $
$Q_{1} =800 \times 4=3200\, J$