What is the condition under which the equation w = PΔV applies?

The equation w = PΔV describes the work done (w) by or on a system in terms of pressure (P) and the change in volume (ΔV). This relationship specifically applies under the condition of constant pressure.

When pressure is held constant, the work done on or by the gas can be easily calculated as the pressure multiplied by the change in volume. If the volume of the system changes (ΔV is non-zero), the work done is simply the product of that change and the constant pressure, which gives a straightforward way to quantify work.

In contrast, if the volume is constant, there’s no change in volume (ΔV = 0), and hence no work is done (w = 0), ruling out the use of this equation. If the temperature is constant, this does not directly relate to the work done in a variable volume context; it’s a different factor relating to the state of the gas. Similarly, the condition of being isolated pertains to the entire system being closed off from work and heat exchange, which also does not apply to the calculation of work in the context described by the equation.