AIIMS 2018 Physics Isothermal Processes MCQ Question

The work done by a gas during isothermal compression can be calculated using the formula $W = -P \Delta V$, where $P$ is the pressure and $\Delta V$ is the change in volume. In this case, the initial volume $V_i = 10 \, \text{L}$ and the final volume $V_f = \frac{10}{15} \, \text{L}$, leading to a change in volume of $\Delta V = V_f - V_i = \frac{10}{15} - 10 = -9.33 \, \text{L}$. Converting this to cubic meters and using the initial pressure $P = 10^5 \, \text{Pa}$, the work done is calculated to be approximately $-2.70 \times 10^3 \, \text{J}$, confirming option A. Other options are incorrect as they either miscalculate the pressure-volume relationship or fail to account for the negative sign associated with work done on the gas during compression.