Entropy & Temperature change with applied Magnetic Field

[pmccunney]

Can someone please help me on relating an induced magnetic field to entropy change, and ultimately a change in material temperature...

Gadolinium (Gd) undergoes a change in entropy when a field of 7.5 Tesla is applied. This process is adiabatic and the initial temperature is 290K.

Im given the entropy and specific heat data but am confused as to how to relate this entropy change to a final temperature.

Im assuming this is an internally reversible process. If so, does the equation Q= integral of TdS apply?

Any help or point in the right direction would be greatly appreciated...

Also i should mention that the mass of Gd is 10kg

thanks!

Homework Equations

The Attempt at a Solution

 

[Mapes]

...am confused as to how to relate this entropy change to a final temperature.

Sounds like a relationship between temperature and entropy, like $\left(\frac{\partial T}{\partial S}\right)_P$, could help, since you could separate the partial differentials and integrate them. Do you know of any physical properties related to this ratio?