# Thermodynamics Questions and Answers – Mixtures of Variable Composition

This set of Thermodynamics Multiple Choice Questions & Answers (MCQs) focuses on “Mixtures of Variable Composition”.

1. For a system of variable composition, the internal energy depends on
a) entropy
b) volume
c) moles
d) all of the mentioned

Explanation: If some substance is added to the system, then energy of the system increases.

2. If the composition of system does not change, then dU=TdS-pdV .
a) true
b) false

Explanation: If the composition changes, then the relation includes many other terms.

3. The molal chemical potential is given by
a) ∂U/∂S
b) ∂U/∂n
c) ∂U/∂V
d) all of the mentioned

Explanation: The molal chemical potential signifies the change in internal energy per unit mole of a component when S,V and number of moles of all other components are constant.

4. The Gibbs entropy equation is given by
a) TdS = dU – pdV – Σ(molal chemical potential)*dn
b) TdS = dU + pdV + Σ(molal chemical potential)*dn
c) TdS = dU + pdV – Σ(molal chemical potential)*dn
d) TdS = dU – pdV + Σ(molal chemical potential)*dn

Explanation: Here summation is taken for all the components present in the system.

5. An equation in Gibbs energy is be given by
a) dG = Vdp + SdT + Σ(molal chemical potential)*dn
b) dG = Vdp – SdT – Σ(molal chemical potential)*dn
c) dG = Vdp + SdT – Σ(molal chemical potential)*dn
d) dG = Vdp – SdT + Σ(molal chemical potential)*dn

Explanation: For this we use G=U+pV-TS and here the summation is taken for all the components present in the system.
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6. The equation written for Gibbs energy can also be written for
a) H
b) F
c) Both of the mentioned
d) None of the mentioned

Explanation: From the equation dG = Vdp – SdT + Σ[(molal chemical potential)*dn], we can write similar equations for F and H..

7. Chemical potential is an extensive property.
a) true
b) false

Explanation: Chemical potential is an intensive property.

8. If the phase of a multi-component system is enlarged, which of the following will happen?
a) U,S and V will increase and T,p and chemical potential will remain same
b) U,S and V will decrease and T,p and chemical potential will remain same
c) U,S and V will increase and T,p and chemical potential will decrease
d) U,S and V will decrease and T,p and chemical potential will increase

Explanation: This depends on the type of property.

9. The Gibbs-Duhem equation is given by
a) SdT + Vdp – Σ(n)*d(molal chemical potential)
b) -SdT + Vdp – Σ(n)*d(molal chemical potential)
c) SdT + Vdp – Σ(n)*d(molal chemical potential)
d) -SdT – Vdp – Σ(n)*d(molal chemical potential)

Explanation: This equation shows the relationship for simultaneous changes in p,T and chemical potential.

10. For a phase which has only one constituent,
a) chemical potential = n/G
b) chemical potential = 1/(G*n)
c) chemical potential = G*n
d) chemical potential = G/n

Explanation: This means that chemical potential is the molar Gibbs function and is a function of p and T only.

11. If a closed system is in equilibrium, which of the following remains constant?
a) entropy
b) volume
c) internal energy
d) all of the mentioned

Explanation: In a closed system, there is no interaction with surroundings hence these quantities along with mass remains constant.

12. At chemical equilibrium, G will be minimum subjected to the equations of constraint.
a) true
b) false

Explanation: This minimum occurs at a constant p and T.

13. The Gibbs phase rule for a non-reactive system is given by
a) f = C + (number of phases) + 2
b) f = C – (number of phases) – 2
c) f = C – (number of phases) + 2
d) f = C – (number of phases) – 2

Explanation: Here f is the variance or the degree of freedom and C is the number of constituents.

14. For a pure substance existing in a single phase,
a) C=1
b) number of phases = 1
c) f=2
d) all of the mentioned

Explanation: Hence we need to know two properties to fix up the state of the system at equilibrium.

15. Which of the following statement is true?
a) if C=1 and number of phases=2, then f=1
b) if C=1 and number of phases=3, then f=0
c) both of the mentioned
d) none of the mentioned

Explanation: This comes from the Gibbs phase rule.

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