To calculate the work done in compressing a gas, you can utilize the formula

where $W$ represents the work done, $P$ is the pressure applied, and $\Delta V$ denotes the change in volume.

When a gas is compressed, work is performed on the gas, leading to a reduction in its volume. The work done on the gas can be quantified using the aforementioned formula. The negative sign in the equation signifies that the work is done on the gas, not by it. This occurs because compression results in a decrease in volume, which typically leads to an increase in the gas’s internal energy.

To apply this formula effectively, you need to know both the initial and final volumes of the gas, as well as the pressure applied during the compression process. If the pressure remains constant throughout the compression, you can calculate the work done simply by multiplying the pressure by the change in volume:

where $V_f$ is the final volume and $V_i$ is the initial volume.

However, if the pressure varies during compression, you will need to employ calculus to integrate the pressure over the change in volume. This can be expressed as:

where $P(V)$ is the pressure as a function of volume.

It’s important to note that the work done in compressing a gas is distinct from the total energy required for the compression process. The energy needed will depend on various factors, including the efficiency of the compression mechanism and any losses that may occur due to friction or heat transfer.