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A furnace wall consists of four layers of different materials, M<sub>1</sub>, M<sub>2</sub>, M<sub>3</sub> and M<sub>4</sub>. 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<br><img src="/images/question-image/metallurgical-engineering/miscellaneous-in-metallurgy/1684344797-M2-B-19-27.PNG" title="Miscellaneous in Metallurgy mcq question image" alt="Miscellaneous in Metallurgy mcq question image">
A
M<sub>1</sub>
B
M<sub>2</sub>
C
M<sub>3</sub>
D
M<sub>4</sub>
Correct Answer:
M<sub>1</sub>
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>
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
$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}t$$
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
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
A furnace wall consists of two layers. The inside layer of 450 mm is made of light weight bricks of thermal conductivity IW/m.K and outside layer of 900 mm is made of refractory of thermal conductivity 2W/m.K. The hot face of the inside layer is at temperature 1300 K and the cold face of the outer layer is at 400 K. The temperature at the interface between the two layers is . . . . . . . . K.
A
1000
B
850
C
700
D
600
A wall has two layers of materials A and B; each made of a different material. Both the layers have the same thickness. The thermal conductivity of materialA is twice that of B. Under the equilibrium, the temperature difference across the wall is 36°C. The temperature difference across the layer A is __________ °C.
A
6
B
12
C
18
D
24
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
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
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
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 m
3
) of the box is
A
0.14
B
0.26
C
0.54
D
0.82
A furnace is made of a refractory brick wall of thickness 0.5 metre and thermal conductivity 0.7 W/m.°K For the same temperature drop and heat loss, this refractory wall can be replaced by a layer of diatomaceous earth of thermal conductivity 0.14 W/m.K and thickness __________ metre.
A
0.01
B
0.1
C
0.25
D
0.5
