Practice Questions on Maxwell Relations with Answers

**Questions on Maxwell Relations with Answers**

*Q1. For a physical system composed of N identical particles confined in space V having energy and entropy S, the pressure P is given by*

*(a) – (∂E/∂V)*_{S,N}*(b) (∂E/∂N)*_{V,S}*(c) (∂E/∂S)*_{N,V}*(d) – (∂S/∂N)*_{V,E}

*Q2. A white star has volume V and contains N electrons so that the density of electrons is n = ^{N}/_{V} . Taking the temperature of the star to be 0 K, the average energy per electron in the star is ∈_{o} = ^{3ℏ2}/_{10m} (3π²n)^{2/3}, write m is the mass of the electron. The electronic pressure in the star is*

*(a) n ∈*_{o}*(b) 2π ∈*_{o}*(c)*^{n}/_{3}∈_{o}*(d)*^{2n}/_{3}∈_{o}

*Q3. If U, F, H, and G represents internal energy, Helmholtz free energy, enthalpy, and Gibbs free energy respectively, then which on of the following is a correct thermodynamic relation ?*

*(a) dU = PdV – TdS**(b) dH = VdP + TdS**(c) dF = -PdV + SdT**(d) dG = VdP + SdT*

*Q4. In an isobaric process the heat intake or release in an thermodynamic system is equal to the change in *

*(a) Helmholtz free energy**(b) Gibbs free energy**(c) Enthalpy**(d) none of these*

**Q5. Which of the following expressions are correct ?**

*(a) dH = TdS + VdP , where H is enthalpy**(b) dF = SdT + PdV , where F is Helmholtz free energy**(c) dG = SdT – VdP , where G is Gibbs function**(d) SdT = TdS + PdV, where E is internal Energy*

*Q6. If Q is the total heat content, E the internal energy, G the Gibbs free energy, F the Helmholtz free energy, T the absolute temperature, P the pressure and C _{p} the molar specific heat of the system at constant pressure, which of the following relations correctly defines C_{p }?*

*(a) (∂H/∂T)*_{P}= C_{P}*(b) (∂G/∂T)*_{P}= C_{P}*(c) (∂E/∂T)*_{P}= C_{P}*(d) (∂F/∂T)*_{P}= C_{P}

*Q7. If E is the energy, G is the Gibbs free energy, F is the Helmholtz free energy and H is the enthalpy for a physical system (N,V,E), then the specific heat at constant pressure is given by *

*(a) (∂G/∂T)*_{N,P}*(b) (∂F/∂T)*_{N,P}*(c) (∂H/∂T)*_{N,P}*(d) (∂E/∂T)*_{N,P}

*Q8. Which of the following is a correct statement of the second law of thermodynamics ?*

*(S = entropy; dQ = energy gained by the system in the form of heat; dW = energy gained by the system in the form of work; T = temperature; F = Helmholtz free energy)*

*(a) dS ≤*^{dQ}/_{T}*(b) dS ≤ 0**(c) dU = dQ + dW**(d) dF ≤ W*

**Q9. If W is the work done on a system in a reversible process and ΔF is the change in its free energy, then**

*(a) W > ΔF**(b) W < ΔF**(c) W = ΔF**(d) W ≠ ΔF*

*Q10. Which of the following is a correct statement of the second law of thermodynamics ?*

*(a) dU = TdS – PdV**(b) W ≥ ΔF**(c) dS =*^{dQ}/_{T}*(d) dS ≤ 0*

*Q11. Let U, T, S and P denote, respectively, the internal energy, temperature, entropy, and pressure of a thermodynamic system. Then a change ΔF in the free energy F = U – TS measures *

*(a) the heat exchanged at constant pressure**(b) the work done by the system at a constant entropy**(c) the work done by the system at a constant temperature**(d) the heat exchanged at a constant temperature*

**Q12. Which of the relation is correct where U is the internal energy, F is the Helmholtz free energy, T is the temperature and V is the volume ?**

*(a) U = T – F(∂F/∂T)*_{v}*(b) U = F + T(∂F/∂T)*_{v}*(c) U = T + F(∂F/∂T)*_{v}*(d) U = F – T(∂F/∂T)*_{v}

*Q13. The internal energy U is related to the Helmholtz free energy F by the relation :*

- (a) U = – T {
^{∂2(F/T)}/_{∂T2}}_{v} - (b) U = T {
^{∂2(F/T)}/_{∂T2}}_{v} - (c) U = – T
^{2}{^{∂(F/T)}/_{∂T}}_{v} - (d) U = T
^{2}{^{∂(F/T)}/_{∂T}}_{v}

**Q14. The free energy for a photon gas is given by F = – ( ^{a}/_{3})VT^{4} , where a is a constant. The entropy S and the pressure P of the photon gas are **

*(a) S =*^{4}/_{3}aVT^{3}, P =^{a}/_{3}T^{4}*(b) S =*^{1}/_{3}aVT^{4}, P =^{4a}/_{3}T^{3}*(c) S =*^{4}/_{3}aVT^{4}, P =^{a}/_{3}T^{3}*(d) S =*^{1}/_{3}aVT^{3}, P =^{4a}/_{3}T^{4}

**Q15. In order to attain thermal equilibrium at a fixed volume, the system minimizes, where the symbols have their usual meaning.**

*(a) S**(b) H = E + pV**(c) G = U – TS + pV**(d) F = U – TS*

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*Answer Key* (if you find any answer wrong, feel free to Correct us)

*Answer Key*

01. | (a) | 06. | (a) | 11. | (c) |

02. | (d) | 07. | (c) | 12. | (d) |

03. | (b) | 08. | (d) | 13. | (c) |

04. | (c) | 09. | (c) | 14. | (a) |

05. | (a) | 10. | (b) | 15. | (d) |