This is the question:
A mineral has a heat capacity Cp which varies in the temperature range 0-2000K according to Cp = 4.0 + 2x10-3T + 3x105T-2. What is the 3rd Law Entropy at 300K?
I am genuinely not really sure how to go about doing this. Since Cp(T) = dQ/dT, dQ = Cp(T)dT. dS = dQ/T so dS = Cp(T)/TdT. So dS = 4.0T-1 + 2x10-3 + 3x105T-3dT. I then thought you'd integrate that between 0K (where S = 0) and 300K but that's not impossible... and to be honest this entire process feels like guesswork anyway.
Could someone give me some pointers? Thanks!