# Work Done by a Gas

When a gas expands it does work on its surroundings. That work is equal to the area under the curve on a P-V diagram which describes that expansion.

Isobaric process:

Process at constant pressure:

W = F D

W = ( F / A ) ( A D )

W = P ( A D )

W = P (V)

Work = area under the curve on a P-V diagram.

Work = area under the curve on a P-V diagram -- even if the process is not isobaric.

Isometric processes:

Isochoric:

Constant volume:

No work is done in an isometric process.

Isothermal process:

Process at constant temperature:

We can keep the temperature constant by having the system in contact with a heat reservoir.

Process with zero heat flow:

Insulated:

The amount of work done will be less than for an isothermal process between the same two volumes. Notice that an adiabat is steeper than an isotherm.

Example:

W = 2.5 atm-l

Now, what is an "atmosphere-liter"? It is a pressure (atm) multiplied by a volume (liter) so it must be some sort of work or energy. Now, this is just a units conversion question,

W = 2.5 atm-l [ 0.001 m3 / 1 l ] [ 1.013 x 105 Pa / 1 atm ]

W = 253 Pa-m3 [ (N/m2) / Pa ]

W = 253 N-m

W = 253 J