Question

a) Consider the hard-sphere gas model. This is an improvement on the ideal gas law that aims to account for the fact that real gas atoms occupy a certain volume and thus exclude other atoms from it. The molar volume of the gas is designated as b. In the hard-sphere gas model, the equation of state is

?(? − ??) = ???

Derive an expression for the work done by the hard-sphere gas in isothermally and reversibly expanding from some initial to some final volume.

b) Now consider a concrete example where one mole of gas expands from 1 L to 2 L at 300 K. Calculate the work done in this reversible and isothermal expansion for both the hard-sphere and the ideal gases. Take b = 1 Å3. Is there a big difference? Roughly speaking, for which gas volumes do you expect there to be a substantial difference?

Answer 1