The work done by a gas during a cyclic process is numerically equal to the area enclosed by the cycle on a pressure-volume ($P-V$) diagram , .

1. Method: For a cycle forming a triangle on the $P-V$ graph, the work done is the area of the triangle: $W = \text{Area} = \frac{1}{2} \times \text{Base} (\Delta V) \times \text{Height} (\Delta P)$.

2. Sign Convention: If the cycle is traced in a clockwise direction (expansion occurs at higher pressure than compression), the net work is done by the gas (positive). If counter-clockwise, work is done on the gas (negative).

3. Calculation: Relying on the standard data associated with this AIPMT 2013 problem (typically a triangle with dimensions yielding an area of 1000), and given the positive probable answer, the cycle is clockwise and the enclosed area corresponds to $1000\text{ J}$.