The work of compression

[missace31]

One mole of a van der Waals gas is compressed quasi-satically and isothermally from volume V[sub:29zwb0mw]1[/sub:29zwb0mw] to V[sub:29zwb0mw]2[/sub:29zwb0mw]. For a van der Waals gas, the pressure is:
p= RT/(V-b)-a/V^2
where a and b are material constants, V is the volume and RT is the gas constant x temperature.

For the first part of the problem I was supposed to write an expression for the work done. According to the equation ?w=-pdV (where w=work, p=pressure, and V=volume) we can solve the equation for work by integrating the pressure equation from V[sub:29zwb0mw]1[/sub:29zwb0mw] to V[sub:29zwb0mw]2[/sub:29zwb0mw]. Doing this, we get:
w=RTln((V_1-b)/(V_2-b))+a(1/V_1 -1/V_2 )

The second part of the question asks: Is more or less work required than for an ideal gas in the low-density limit? What about the high-density limit? Why?
Basically, I don't understand what the second part of the question is asking. Any help would be much appreciated! Thanks.

(Sorry, I tired to format the equations in Microsoft equation editor first so they'd look normal, but it didn't work.. I don't know how to do that on here :-/ )

 

[missace31]

I'm still confused as to the second part of this problem. However, I have had another thought but still lack the ability to execute it. I am wondering if when the questions asks the difference in work between the low density limit and the high density limit if it is asking about the limits of integration V[sub:2rv4tl1n]1[/sub:2rv4tl1n] and V[sub:2rv4tl1n]2[/sub:2rv4tl1n]. If this were to be the case then my confusion then would lie it how to execute this. For instance, would we want to first evaluate the limit from 0 to V[sub:2rv4tl1n]1[/sub:2rv4tl1n] and compare that to when we evaluate the limit from V[sub:2rv4tl1n]1[/sub:2rv4tl1n] to V[sub:2rv4tl1n]2[/sub:2rv4tl1n]. I'm not sure if this would answer exactly what the question is asking.