In the hypothetical phase diagram, the melting point of each pure component is. 1000 K and the eutectic temperature is 800 K. The eutectic is located at the equi-atomic composition. The maximum solid solubility in α-phase is given by the mole fraction, Ne = 0.1. The freezing range (in K) of the alloy with composition, Ne = 0.1 is <img src="/images/question-image/metallurgical-engineering/physical-metallurgy/1684342050-M2-B-7-80.PNG" title="Physical Metallurgy mcq question image" alt="Physical Metallurgy mcq question image">

An alloy of overall composition, X_B = 0.7 was equilibrated at temperature T₁. Microstructural analysis showed two phases, (α and β, and that the phase fraction of β was 0.75. Given that the equilibrium composition of β at Ti is 0.9 as shown in the phase diagram below, the maximum solubility of B in α (in mole fraction) at this temperature is . . . . . . . .

A

0.05

B

0.10

C

0.50

D

0.85

The diffusion couple shown below is made from two A-B alloys. The initial compositions of the two alloys are indicated in the diagram. The centreline is at x = 0. The couple is held at an elevated temperature for 40 hours. Diffusivity; D = 3 × 10^-11 m^-2 s^-1. Assume the diffusion couple to be infinitely long.

Which of the parameters give the composition profile in the following form?
$$C\left( {x,t} \right) + {c_1} + {c_2}\,erf\left( {\frac{1}{{2\sqrt {Dt} }}} \right)$$

A

c1 = 0.45, c2 = 0.05

B

c1 = 0.5, c2 = 0.4

C

c1 = -0.05, c2 = 0.45

D

c1 = 0.1, c2 = 0.9

It is desired to freeze 10,000 loaves of bread each weighing 0.75 kg from an initial room temperature of 18°C to a final temperature of -18°C. The bread-freezing operation is to be carried out in an air-blast freezing tunnel. It is found that the fan motors are rated at a total of 80 horsepower and measurements suggest that they are operating at around 90% of their rating, under which conditions their manufacturer’s data claims a motor efficiency of 86%. If 1 ton of refrigeration is 3.52 kW, estimate the maximum refrigeration load imposed by this freezing installation assuming that fans and motors are all within the freezing tunnel insulation and the heat-loss rate from the tunnel to the ambient air has been found to be 6.3 kW. Extraction rate from freezing bread (maximum) = 104 kW

A

46 tons of refrigeration

B

40 tons of refrigeration

C

56 tons of refrigeration

D

50 tons of refrigeration

One cubic meter of some alloy is heated in a crucible from room temperature to 100 degree Celsius above its melting point for casting. The alloy density = 7.5 g/cm3, melting point = 800 0C, specific heat = 0.33 J/gC in the solid state and 0.29 J/gC in liquid state and heat of fusion = 160 J/g. How much heat energy must be added to accomplish the heating, assuming no losses? Ambient temp = 25 °C. Density of solid and liquid are same.

A

4535 * 106J

B

8735 * 106J

C

9135 * 106J

D

7835 * 106J

An elliptical dislocation loop is gliding on plane ABCD of a single crystal of BCC material as shown in the following figure. It is gliding along the burger vector 'b'. Identify the correct statement.

P. Plane ABCD belongs to the family of (110).
Q. Burger vector 'b' belong to direction.
R. Dislocation has the edge character at point x and the screw character at point z.
S. Dislocation has the screw character at point x

A

P, Q

B

Q, R

C

P, R

D

P, S

Thin layer of material B (of total amount m) is plated on the end faces of two long rods of material A. These are then joined together on the plated side (see the figure below) and heated to a high temperature. Assuming the diffusion coefficient of B in A is D, the composition profile CB along the rod axis x after a time t is described by

A

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}\exp \left$$

B

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}erf\left$$

C

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}\left$$

D

$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}t$$

A furnace wall is made of three materials (I, II and III) of equal thickness and having thermal conductivity k₁ k₂ and k₃ respectively. The steady state temperature profile inside each material is shown in the figure. Thermal conductivities of the materials will vary as

A

k1 > k2 > k3

B

k2 > k1 > k3

C

k3 > k1 > k2

D

k3 > k2 > k1

From a 2 m × 1.2m sheet, squares are Cut out from each of the four comers as shown in the figure and then the sides are bent to form an open box. The maximum possible volume (in m³) of the box is

A

0.14

B

0.26

C

0.54

D

0.82

A simplified energy band-diagram of an intrinsic semiconductor at thermal equilibrium (300 K) is shown. In the accompanying table, which one of the four cloumns correctly represents the listed parameters? Assume same effective mass for electrons and holes.

A

<table class="table-style-1"> <tr> <td rowspan="2">Parameter</td> <td colspan="4">Energy-difference</td> </tr> <tr> <td>Column 1</td> <td>Column 2</td> <td>Column 3</td> <td>Column 4</td> </tr> <tr> <td>Band-gap</td> <td>ΔE2</td> <td>ΔE1</td> <td>ΔE2</td> <td>ΔE1</td> </tr> <tr> <td>Electron affinity</td> <td>$$\frac{{\Delta {E_1}}}{2}$$</td> <td>ΔE2 - ΔE1</td> <td>$$\frac{{\Delta {E_2}}}{2}$$</td> <td>ΔE2 - $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> </tr> <tr> <td>Work function</td> <td>ΔE1 + ΔE2</td> <td>ΔE2 - $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> <td>ΔE1 - $$\frac{{\Delta {E_2}}}{2}$$</td> <td>ΔE2 + $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> </tr></table> Column 1

B

Column 2

C

Column 3

D

Column 4

Match the heat treatment for an eutectoid steel shown in the TTT diagram below (as P, Q, R and S) with the resulting microstructure listed below:
1. Fine pearlite
2. martensite
3. Bainite
4. Coarse pearlite

A

P-1, Q-2, R-4, S-3

B

P-4, Q-1, R-3, S-2

C

P-2, Q-1, R-3, S-4

D

P-1, Q-4, R-3. S-2