# Question of Work with non-ideal gas expansion

1. Feb 11, 2010

### Fwahm

1. The problem statement, all variables and given/known data

Consider a system described by the van der Waals equation of state which expands at constant temperature from volume V1 to volume V2. Assume that the density g= N/V ≪ 1 over the range of volumes of interest.

(a) Calculate the work Wvdw done on the gas to the lowest relevant order in g.

(b) Calculate the work Wideal done on the gas under the same conditions assuming that the gas is ideal.

(c) Find the difference Wvdw − Wideal and discuss the reason why this difference is positive or negative as a function of the temperature.

2. Relevant equations

(P +aN2/V2)(V − Nb) = NkT

dW = -PdV

3. The attempt at a solution

I've already determined the answer to b, but I'm not sure how to get the work done on the gas in a non-ideal situation, described by the Van der Waals equation of state. In addition, I'm not sure what (a) means when it refers to the lowest relevant order in g.