Answer
$564\;\rm J$
Work Step by Step
For an ideal gas in a Carnot engine is having a closed cycle in four processes, two isothermals, and two diabetics.
There is no heat exchange during the two adiabatic processes.
We are given that the expansion isothermal process occurs at $T_H=300^\circ\rm C$ while the compression isothermal process occurs at $T_C=50^\circ \rm C$.
We need to find the heat exhausted $Q_C$ in the compression isothermal process, which is given by
$$Q_H=W_{\rm out}+Q_C$$
where we know that $Q_H=1000$ J during the isothermal expansion process.
Thus,
$$Q_C=Q_H-W_{\rm out} \tag 1$$
Now we need to find $W_{\rm out}$ where we know that the thermal efficiency of the Carnot engine is given by
$$\eta=\dfrac{W_{\rm out}}{Q_H}=1-\dfrac{T_C}{T_H}$$
Thus,
$$W_{\rm out}=\dfrac{Q_H(T_H-T_C)}{T_H}$$
Plugging into (1) and then plugging the known;
$$Q_C=Q_H- \dfrac{Q_H(T_H-T_C)}{T_H}=1000- \dfrac{1000([300+273]-[50+273])}{[300+273]}$$
$$Q_C= \color{red}{\bf 564}\;\rm J$$
