The efficiency of a heat engine is $\eta = 40\%$. In one cycle the engine takes a quantity of heat $Q_1 = 1000$ J from the heater. Find the work done by the engine in one cycle.
The efficiency of a heat engine is the ratio of the work done to the heat taken in:
$$\eta = \frac{A}{Q_1} \Rightarrow A = \eta Q_1$$
$$A = 0.4 \cdot 1000 = 400 \text{ J}$$
$A = 400$ J