How Do I Solve Part (b) of Problem 5.17 in Schroeder's Thermal Physics?

[touqra]

This is really not a homework question. I'm learning thermal physics by Schroeder (2000) myself.
I'm stuck at Problem 5.17 page 160.

I can get Part (a) but Part (b), subtracting off the work that would be required even if the specimen were not present. I subtracted the work $$\frac{B}{\mu_0} dB$$ but it wasn't correct...

 

[blochwave]

I'm sure someone has the book but I'd probably have an easier time if I had, you know, the problem