To calculate the work done during the expansion of a gas, we utilize the formula:

When a gas expands, it performs work on its surroundings. This work is defined as the product of the force exerted by the gas and the distance over which that force acts. The force exerted by the gas is equivalent to its pressure, and the distance corresponds to the change in volume of the gas. Thus, the work done by the gas can be expressed as:

In this equation, $P$ represents the pressure of the gas, and $\Delta V$ denotes the change in volume.

It is crucial to ensure that the pressure and volume are expressed in compatible units for the formula to yield accurate results. Additionally, the sign of the work done by the gas is significant: it is considered positive when the gas expands and negative when it is compressed. This distinction arises because work is defined as the transfer of energy between systems. When a gas expands, it transfers energy to its surroundings, resulting in positive work. Conversely, during compression, the gas receives energy from its surroundings, leading to negative work.

Overall, the formula

serves as an essential tool for calculating the work done during gas expansion and can be applied across various fields, including thermodynamics and engineering.