# Questions on Maxwell Relations with Answers

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/3o
• (d) 2n/3o

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 Cp the molar specific heat of the system at constant pressure, which of the following relations correctly defines Cp ?

• (a) (∂H/∂T)P = CP
• (b) (∂G/∂T)P = CP
• (c) (∂E/∂T)P = CP
• (d) (∂F/∂T)P = CP

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 = – T2 {∂(F/T)/∂T }v
• (d) U = T2 {∂(F/T)/∂T }v

Q14. The free energy for a photon gas is given by F = – (a/3)VT4 , where a is a constant. The entropy S and the pressure P of the photon gas are

• (a) S = 4/3 aVT3 , P = a/3 T4
• (b) S = 1/3 aVT4 , P = 4a/3 T3
• (c) S = 4/3 aVT4 , P = a/3 T3
• (d) S = 1/3 aVT3 , P = 4a/3 T4

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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