What is the equation for calculating work done when a gas expands and moves a piston?

The equation for calculating work done during the expansion of a gas that moves a piston relies on the interaction between the gas and its surroundings. In this scenario, the external pressure plays a crucial role. When a gas expands, it does work against the external atmosphere or any opposing pressure, which is why the work done is defined as the external pressure multiplied by the change in volume of the gas.

This relationship arises from the principle that work is done when a force is applied over a distance. In this case, the force exerted by the gas on the piston is a result of the pressure it exerts on the piston surface area, and the piston moves a distance equal to the change in volume. Hence, the correct formulation of work done is the product of the external pressure and the change in volume of the gas during the expansion process.

This reasoning aligns with the conventions typically used in thermodynamics, where work done by the system (in this case, the gas) is taken to be positive when the system expands and does work against external pressures. Consequently, understanding the significance of external pressure in this context is key to correctly applying the formula.