ME Thermodynamics and Kinetics of Materials 1 — Questions and Answers
Question 1: The Gibbs free energy change (ΔG) for a reaction at constant temperature and pressure determines spontaneity. Which condition indicates a spontaneous process?
- ΔG > 0
- ΔG = 0
- ΔG < 0 (Correct answer)
- ΔH > 0
Correct answer: ΔG < 0
A negative ΔG (ΔG < 0) means the process releases usable energy and proceeds spontaneously at constant T and P.
Question 2: According to the Gibbs phase rule, for a binary system at equilibrium, the number of degrees of freedom F is given by:
- F = C + P - 2
- F = C - P + 2 (Correct answer)
- F = P - C + 2
- F = C + P + 2
Correct answer: F = C - P + 2
The Gibbs phase rule is F = C - P + 2, where C is the number of components and P is the number of phases.
Question 3: Which thermodynamic quantity directly relates the chemical potential of a component to its activity in a solution?
- μ = μ° + RT ln(a) (Correct answer)
- μ = μ° - RT ln(a)
- μ = μ° + RT/a
- μ = μ° × RT × a
Correct answer: μ = μ° + RT ln(a)
The chemical potential μ equals the standard chemical potential μ° plus RT times the natural log of activity a.
Question 4: For an ideal solution of two metals, the enthalpy of mixing (ΔH_mix) is:
- Always positive
- Always negative
- Zero (Correct answer)
- Equal to TΔS_mix
Correct answer: Zero
In an ideal solution, interactions between unlike atoms are identical to like-atom interactions, so ΔH_mix = 0 and mixing is driven entirely by entropy.
Question 5: The Clausius-Clapeyron equation describes the relationship between pressure and temperature along a phase boundary. For most metals, the solid-liquid boundary has a slope (dP/dT) that is:
- Negative
- Zero
- Positive and very steep (Correct answer)
- Positive and shallow
Correct answer: Positive and very steep
For most metals, the solid is denser than the liquid, giving a large positive dP/dT slope on the solid-liquid phase boundary.
Question 6: Which expression correctly defines the equilibrium constant K for a chemical reaction in terms of standard Gibbs free energy change ΔG°?
- ΔG° = RT ln K
- ΔG° = -RT ln K (Correct answer)
- ΔG° = -RT/ln K
- ΔG° = RT/K
Correct answer: ΔG° = -RT ln K
The standard Gibbs free energy change is related to the equilibrium constant by ΔG° = -RT ln K.
Question 7: In a regular solution model, the excess Gibbs free energy (G^E) compared to an ideal solution is attributed to:
- Excess entropy of mixing only
- Excess enthalpy of mixing only (Correct answer)
- Both excess enthalpy and excess entropy of mixing
- Neither enthalpy nor entropy contributions
Correct answer: Excess enthalpy of mixing only
In the regular solution model, the excess entropy is assumed to be zero and G^E arises solely from a non-zero enthalpy of mixing.
ME Thermodynamics and Kinetics of Materials 1
The Gibbs free energy change (ΔG) for a reaction at constant temperature and pressure determines spontaneity.
Which condition indicates a spontaneous process?