4. Multiple choice A. The following differential equation (-) (au/a(oG/aPh nR(dH

Question

4. Multiple choice A. The following differential equation (-) (au/a(oG/aPh nR(dH/aS)e represents: a) work done on a gas at constant temperature b) fugacity of a nonideal gas c) the chemical potential of an ideal gas d) the ideal gas law B. The derivation of the Maxwell relationships was based upon the observation that: a) most thermodynamic systems are nonideal b) gases expand when heated c) thermodynamic state functions are exact differentials d) entropy is based upon probability C. The Maxwell relationships are useful in thermodynamics because: a) they are used in gas compression technology b) they may simplify formulas to contain only measurable quantities c) they can predict the spontaneity of processes d) they led to the concept of fugacity D. Chemical potential represents change in_divided by change in a) entropy, volume b) enthalpy, pressure c) Gibbs Free Energy, number of moles d) Gibbs Free Energy, fugacity E. In deriving the Gibbs-Helmholtz formula, which substitution was made to eliminate entropy from the formula: a) ds-da/T S--OG/OTp) c) S =-(dA/dTlv d) S-K In

Explanation / Answer

4.(A) From the eqn dU=Tds-Pdv ; -(U/V)s = P

dG= -SdT+VdP ; (G/P)T = V

dH = Tds +VdP ; (H/S)p =T

So overall equation PV = nRT represents ideal gas equation.

(B) The derivation of maxwell relationships was based upon the observation that - (c) thermodynamic state functions are exact differentials.

(C) The maxwell relationships are useful in thermodynamics because - (c) they can predict the spontaneity of the processes.

(D) Chemical potential represents change in Gibb's free energy divided by number of moles.

(E) In deriving Gibb's Helmotz formula entropy is eleminated by S = - (G/T)P

For derivation , we start from G=H-TS

Then -S= (G-H)/T

then S is replaced by -(G/T)P and expression becomes (G/T)P = (G-H)/T

Then we by differentiating (G/T) with respect to T and comparing with above equation we will get the Gibb's Helmotz equation. [ ref. Physical chemistry, G.W. Castellan, 3rd ed. p216]

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