1. The problem statement, all variables and given/known data Find the equation of state given that k = aT^(3) / P^2 (compressibility) and B = bT^(2) / P (expansivity) and the ratio, a/b? 2. Relevant equations B = 1/v (DV /DT)Pressure constant ; k = -1/v (DV /DP)Temperature constant D= Partial derivative dV = BVdT -kVdP (1) ANSWER is V = V0exp(aT^(3)/P) 3. The attempt at a solution a. Integrate (1) and obtain v = voexp (bT^(3)/3P) + 2aT^(3)/P^3) WRONG b. Hint by Professor: rewrite as: (Let "D" = partial derivative): D/DP (lnV) = 1/V (DV/DP) then D/DP (lnV) + aT^(3)/P = 0. Write as D/DP(lnv + g(P,T)) = 0 where g is a function only of V. ==> lnV + g(P,T) = f(V) where V is an arbitrary function. I don't understand "b" but following attempt "a" gave me the proper result for a very similar problem?