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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<sup>-11</sup> m<sup>-2</sup> s<sup>-1</sup>. Assume the diffusion couple to be infinitely long.<br><img src="/images/question-image/metallurgical-engineering/physical-metallurgy/1684342519-M2-B-7-82.PNG" title="Physical Metallurgy mcq question image" alt="Physical Metallurgy mcq question image"><br>Which of the parameters give the composition profile in the following form?<br>$$C\left( {x,t} \right) + {c_1} + {c_2}\,erf\left( {\frac{1}{{2\sqrt {Dt} }}} \right)$$
A
c<sub>1</sub> = 0.45, c<sub>2</sub> = 0.05
B
c<sub>1</sub> = 0.5, c<sub>2</sub> = 0.4
C
c<sub>1</sub> = -0.05, c<sub>2</sub> = 0.45
D
c<sub>1</sub> = 0.1, c<sub>2</sub> = 0.9
Correct Answer:
c<sub>1</sub> = 0.45, c<sub>2</sub> = 0.05
An alloy of overall composition, X
B
= 0.7 was equilibrated at temperature T
1
. 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
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 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><strong>Column 1</strong></td> <td><strong>Column 2</strong></td> <td><strong>Column 3</strong></td> <td><strong>Column 4</strong></td> </tr> <tr> <td>Band-gap</td> <td>ΔE<sub>2</sub></td> <td>ΔE<sub>1</sub></td> <td>ΔE<sub>2</sub></td> <td>ΔE<sub>1</sub></td> </tr> <tr> <td>Electron affinity</td> <td>$$\frac{{\Delta {E_1}}}{2}$$</td> <td>ΔE<sub>2</sub> - ΔE<sub>1</sub></td> <td>$$\frac{{\Delta {E_2}}}{2}$$</td> <td>ΔE<sub>2</sub> - $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> </tr> <tr> <td>Work function</td> <td>ΔE<sub>1</sub> + ΔE<sub>2</sub></td> <td>ΔE<sub>2</sub> - $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> <td>ΔE<sub>1</sub> - $$\frac{{\Delta {E_2}}}{2}$$</td> <td>ΔE<sub>2</sub> + $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> </tr></table> Column 1
B
Column 2
C
Column 3
D
Column 4
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
A
100
B
130
C
160
D
190
A furnace wall is made of three materials (I, II and III) of equal thickness and having thermal conductivity k
1
k
2
and k
3
respectively. The steady state temperature profile inside each material is shown in the figure. Thermal conductivities of the materials will vary as
A
k<sub>1</sub> > k<sub>2</sub> > k<sub>3</sub>
B
k<sub>2</sub> > k<sub>1</sub> > k<sub>3</sub>
C
k<sub>3</sub> > k<sub>1</sub> > k<sub>2</sub>
D
k<sub>3</sub> > k<sub>2</sub> > k<sub>1</sub>
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
A furnace wall consists of four layers of different materials, M
1
, M
2
, M
3
and M
4
. If the layers are of equal thickness and the steady state temperature profiles is as shown below, then the material with the lowest thermal conductivity is
A
M<sub>1</sub>
B
M<sub>2</sub>
C
M<sub>3</sub>
D
M<sub>4</sub>
A square of 9 mm
2
area is subjected to simple shear displacement √3 mm along x-direction, as shown below: The strain imparted will be
A
$$\frac{1}{3}$$
B
$$\frac{1}{{\surd 3}}$$
C
$${\surd 3}$$
D
3
Engineering stress-strain curve for a metal under two conditions. A and B, are shown is the following figures. Identify the correct statement.
A
The resilience of the material is the same in conditions A and B
B
The resilience of the material is higher in condition B than in condition A
C
The toughness of the material is higher in condition A than in condition B
D
The toughness of the material is higher in condition B than in conditon A
An infinitely long wire carrying a current $$I\left( t \right) = {I_0}\cos \left( {\omega t} \right)$$ is placed at a distance a from a square loop of side a as shown in the figure. If the resistance of the loop is R, then the amplitude of the induced current in the loop is
A
$$\frac{{{\mu _0}}}{{2\pi }} \cdot \frac{{a{I_0}\omega }}{R}\ln 2$$
B
$$\frac{{{\mu _0}}}{\pi } \cdot \frac{{a{I_0}\omega }}{R}\ln 2$$
C
$$\frac{{2{\mu _0}}}{\pi } \cdot \frac{{a{I_0}\omega }}{R}\ln 2$$
D
$$\frac{{{\mu _0}}}{{2\pi }} \cdot \frac{{a{I_0}\omega }}{R}$$
