I'm not entirely sure whether this belongs in this section or in the "differentiation" section, so sorry in advance if it should be elsewhere...
Basically i'm pretty stuck with a question on partial derivatives, related to the enthalpy of a gas. It goes as follows.
Enthalpy of a gas is defined by H = U + pV , where U satisfies dU = TdS-pdV. First thing is to find a relationship between the differentials of H, S and p - which is fine - dH = TdS + Vdp.
The next part's where i'm stuck - and i'll apologise in advance, i've not mastered the maths fonts yet. It says 'by regarding U as a function of p and V (i.e. i think using dU = TdS-pdV...?) and considering 2 expressions for
(from here below, all d's are partial derivatives, ie. 'del')
(d^2 U)/(dpdV)
show that
(ds/dv)*(dT/dp) - (ds/dp)*(dT/dV) = 1'
Given that (dV/ds) = (dT/dS)
I've literally no idea what it means, or how to proceed. Something tells me to rewrite the expression for dU by using differential expression for dS, but i've no idea if that's right. Any help would be massively appreciated, especially if you can make head or tail of what i've actually written! - once again, apologies for not having mastered the maths font thing, i did try...
Edit: I should be clear - by (d^2U/dVdp) i mean a 2nd partial derivative, i.e. the mixed 2nd partial derivative here.