In: Chemistry
Starting with the exact differential for S (entropy, treated as a state function of P, pressure, and T, temperature), the definition of entropy, S, definition of heat, q, and the definition of enthalpy, H, show that
dS= (Cp/T)dT - alpha*V*dP
where
alpha= (1/V)*(dV/dT) when P is held constant
.Using the Helmholtz free energy, A, given by
A=U - TS
express dS in terms of dT and dV