Work done by the gas on the piston

When a gas pushes a piston of area $A$ through a distance $\Delta h$, it does work. Since the force exerted by the gas is $F_\text{gas} = P_\text{gas}\cdot A$, the work is

$L_\text{gas} = F_\text{gas}\cdot\Delta h = P_\text{gas}\cdot A\cdot\Delta h = P_\text{gas}\cdot\Delta V$

where $\Delta V = A\,\Delta h$ is the change in the gas’s volume. This formula holds when the gas pressure remains constant during the displacement (isobaric process).

Watch the signs

$L_\text{gas}$ is the work done by the gas on the piston.

• If the piston rises (gas expanding), $\Delta V > 0$ and $L_\text{gas} > 0$: the gas gives energy to the environment.
• If the gas is compressed, $\Delta V < 0$ and $L_\text{gas} < 0$: the gas receives energy.

The intuition is that of a push along a displacement: the gas “pushes” the piston outwards, and like any force acting in the direction of the displacement, it does positive work, giving up energy. If instead it is the outside that pushes the piston in, compressing the gas, the work done by the gas is negative and energy enters the gas.

Collegamenti

Argomenti: Teoria cinetica dei gas · Termodinamica Concetti: Pressione · Lavoro di una forza

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