When calculating the work done during gas compression, how is the external pressure treated?

When considering the work done during gas compression, the external pressure is treated as positive. This is because work is defined in thermodynamics as the product of force times distance, and in the context of a gas being compressed, the system (the gas) is doing work against the external pressure.

In a compression process, the gas's volume decreases, which requires energy to be applied to counteract the force exerted by the external pressure. This positive value reflects that work is being done on the system. Hence, when calculating the work done on the gas during compression, the external pressure is treated as a positive quantity, influencing the work calculation accordingly.

Using the formula for work done, ( W = - P_{ext} \Delta V ), where ( \Delta V ) is negative for compression (since it decreases in volume), the negative sign accounts for the work being done on the system, thereby resulting in a positive work value (from the external pressure being positive) that shows energy is entering the system.