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1. What is Gibbs phase rule for general system?
a) P = C – 1 – F
b) P = C + 1 – F
c) P + F = C – 2
d) P + F = C + 2

Answer: d [Reason:] The number of degrees of freedom, F (no. of independently variable factors), number of components, C, and number of phases in equilibrium, P.

2. What is Gibbs phase rule for metallurgical system?
a) F = C – 1 – P
b) F = C + 1 – P
c) P + F = C – 2
d) P + F = C + 2

Answer: b [Reason:] For metallurgical system pressure has no appreciable effect on phase equilibrium and hence, F = C – P + 1.

3. In a single – component condensed system, if degree of freedom is zero, maximum number of phases that can co – exist _________
a) 2
b) 3
c) 0
d) 1

Answer: a [Reason:] Given F = 0 Then p = c + 1, c = 1 .: P = 2.

4. The degree of freedom at triple point in unary diagram for water is________
a) 2
b) 3
c) 0
d) 1

Answer: c [Reason:] For three phase system degree of freedom is 0.

5. What is degree of freedom for single – phase fields on the phase diagram?
a) 2
b) 3
c) 0
d) 1

Answer: a [Reason:] F = C + 1 – P F = 3 – P (C = 2) .:F = 2.

6. What is degree of freedom when two phases co – exist?
a) 2
b) 3
c) 0
d) 1

Answer: d [Reason:] F = C + 1 – P F = 3 – P (C = 2) F = 3 – 2 = 1.

7. What is degree of freedom when three phases co – exist?
a) 2
b) 3
c) 0
d) 1

Answer: c [Reason:] F = C + 1 – P F = 3 – P (C = 2) F = 3 – 3 = 0.

8. For single component system when degree of freedom is 1(one) then number of phases _______
a) 2
b) 3
c) 0
d) 1

Answer: d [Reason:] F = C + 1 – P F = 2 – P (C = 1) → p = 2 – F = 2 – 1 = 1.

Analyze the figure and answer the following questions 9. When α, L and β phasefields touch the isotherm linewhat are the respective phase compositions?
a) 8.0 wt%, 71.9 wt%, 91.2 wt% of Ag
b) 8.0 wt%, 91.2 wt%, 71.9 wt% of Ag
c) 71.9 wt%, 91.2 wt%, 8.0 wt% of Ag
d) 91.2 wt%, 8.0 wt%, 71.9 wt% of Ag

Answer: a [Reason:] For binary systems, when three phases are present, there is no F, so composition is fixed.

10. For binary alloy consisting of three phases of non – equilibrium one, then temperature of these phases will be _______
a) Different
b) Constant
c) Same
d) Two of them will be with one temperature