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Consider the four equations of states(EOS) below describing PVT behavior of gases. Let a and b be constants. EOSI : PV = RT EOSII: (P-a)V = RT EOSIII: P(V-b) = RT EOSIV: P = RT/(V-b) - a/V (a) Prove for EOSI that both U and H are functions of T only. (b) Prove for EOSII that H is a function of T only, but U is a function of multiple variables. (c) Prove for EOSIII that U is a function of T only, but H is a function of multiple variables. (d) Prove for EOSIV that U is not a function of T only.