Categories

# Pressure-volume work: Work done by a gas

Gases can do work through expansion or compression against a constant external pressure. Work done by gases is also sometimes called pressure-volume or PV work for reasons that will hopefully become more clear in this section!Let’s consider gas contained in a piston. If the gas is heated, energy is added to the gas molecules. We can observe the increase in average kinetic energy of the molecules by measuring how the temperature of the gas increases. As the gas molecules move faster, they also collide with the piston more often. These increasingly frequent collisions transfer energy to the piston and move it against an external pressure, increasing the overall volume of the gas. In this example, the gas has done work on the surroundings, which includes the piston and the rest of the universe.To calculate how much work a gas has done (or has done to it) against a constant external pressure, we use a variation on the previous equation:

work = w = -Pexternal × ΔV

where Pexternal  is the external pressure (as opposed to the pressure of the gas in the system) and ΔV is the change in the volume of the gas, which can be calculated from the initial and final volume of the gas:

ΔV = Vfinal – Vinitial

Since work is energy, it has units of Joules(where 1 Joule = 1 kg.mm2 / s2)  You may also see other units used, such as atmospheres for pressure and liters for volume, resulting in L . atm, as the unit for work. We can convert L⋅atm, to convert to Joules using the conversion factor of 101.325J/ 1L.atm.

### The sign of work

As a matter of convention, negative work occurs when a system does work on the surroundings.

• When the gas does work the volume of a gas increases (\Delta \text V>0ΔV>0delta, start text, V, end text, is greater than, 0) and the work done is negative.
• When work is done on the gas, the volume of the gas decreases (\Delta \text V<0ΔV<0delta, start text, V, end text, is less than, 0) and work is positive.

One way to remember the sign convention is to always think about the change in energy from the point of view of the gas. When the gas expands against an external pressure, the gas has to transfer some energy to the surroundings. Thus, the negative work decreases the overall energy of the gas. When the gas is compressed, energy is transferred to the gas so the energy of the gas increases due to positive work.