(a) Give the definition of the partial molar volume VJ, and write down dV (differential of the total volume) for a binary mixture of A and B in terms of all independent physical variables. (b) Prove that for a binary mixture of A and B at constant T and p, the total volume is given as V=nAVA+nBVB (the procedure needs to be specified) (c) What is the definition of the chemical potential (J) for the Jth component in a mixture? According to the expression above, the total Gibbs energy and J 's for all the components (J) is related. Write out this expression