The work done during an isothermal process can be expressed using the formula:

In an isothermal process, the temperature remains constant. This constancy allows us to employ the ideal gas law, which relates pressure, volume, and the number of moles of gas. The work done in a thermodynamic process is also represented by the equation:

where $P$ denotes pressure and $\Delta V$ represents the change in volume.

To calculate the work done in an isothermal process, we leverage the fact that, since the temperature is constant, pressure and volume are inversely proportional. This relationship can be expressed as:

By substituting $P_1 V_1$ for $P_2 V_2$ in the work equation, we obtain:

Next, we can apply the ideal gas law, which states that $P_1 V_1 = nRT$. By substituting this relationship into our work equation, we arrive at the final expression for work done in an isothermal process:

This formula succinctly captures the work performed by or on an ideal gas during an isothermal expansion or compression.