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Now In this particular Post of IIT JAM Physics Test Series, you will get a test of the topic Thermodynamic Potentials and Maxwell Relation of Chapter Kinetic Theory and Thermodynamics. There are total 15 Questions given below also Answers are attached at the end of the test so that you can verify your answers after completing the test. So, Practice these Questions and Do your Best. Also Solve **IIT JAM Physics Previous Year Question Paper**. And Don’t Forget to Share with Your Friends.

**[Free] IIT JAM Physics Test Series 2023 : Kinetic Theory and Thermodynamics- ***(Thermodynamic Potentials and Maxwell Relation)*

*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) |

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