## Pressure-Volume Work

When a gas is compressed, work is obviously being done TO the system (so ΔW is positive). The formula for how much work is done is:

Pext is the external pressure ... the amount of pressure that the surroundings are applying to the system.

ΔV is the change in volume (in Litres) that the system experiences.

Do NOT forget the negative sign. It is needed so that a COMPRESSION (decrease in volume) corresponds to work being done TO the system.

It is also important to remember that 1 J = 1 L atm. If you put Pext in atm, and ΔV in Litres, then your answer will be in Joules.

ΔV is the change in volume (in Litres) that the system experiences.

Do NOT forget the negative sign. It is needed so that a COMPRESSION (decrease in volume) corresponds to work being done TO the system.

It is also important to remember that 1 J = 1 L atm. If you put Pext in atm, and ΔV in Litres, then your answer will be in Joules.

## Sample Question

Q: How much work is done on a balloon that is compressed from 6 L to half its original volume at atmospheric pressure?

A: Well:

304 J of work is done to the balloon.

A: Well:

- Convert pressure from atm to kPa, so Pext = 101.325 kPa

ΔV = Vfinal - Vinitial = 3 L - 6 L = -3 L. - This may seem obvious, since the balloon obviously loses 3 L of volume.
- So, ΔW = -Pext(ΔV) = -(101.3 kPa)(-3 L) = 304 L kPa = 304 J

304 J of work is done to the balloon.

*Shout-out to [a student, name withheld pending permission] from Arizona State for catching an error I made here earlier! Corrected March 11, 2013.*