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 ........... $J$
JEE MAIN 2021, Medium
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$\eta=\frac{ T _{2}}{ T _{1}}=\frac{ Q _{2}}{ Q _{1}}=\frac{ Q _{1}- W }{ Q _{1}} \quad\left(\because W = Q _{1}- Q _{2}\right)$
$\frac{400}{800}=1-\frac{ W }{ Q _{1}}$
$\frac{ W }{ Q _{1}}=1-\frac{1}{2}=\frac{1}{2}$
$Q _{1}=2 W =2400 J$
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