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GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper
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© examsnet.com
Question : 55
Total: 65
A steel part with surface area of
125
c
m
2
is to be chrome coated through an electroplating process using chromium acid sulphate as an electrolyte. An increasing current is applied to the part according to the following current time relation:
I
=
12
+
0.2
t
where
I
=
current
A
. and
t
=
time (minutes). The part is submerged in the plating solution for duration of 20 minutes for plating purpose. Assuming the cathode efficiency of chromium to be
15
%
and the plating constant of chromium acid sulphate to be
2.50
×
10
−
2
m
m
/
A
−
s
, the resulting coating thickness on the part surface is ________ µm (round off to one decimal place).
Your Answer:
Validate
Solution:
Given
As
=
125
c
m
2
A
s
=
125
×
10
2
m
m
2
(
η
)
cathode
=
0.15
I
=
12
+
0.2
t
t
=
20
minutes.
C (Plating Constant)
"
=
B
.5
×
10
−
2
m
m
3
/
As
C
=
A
.5
m
m
3
/
A
m
i
n
Since current is changing with time we have to Integrate
T
→
thickness of coating
d
T
d
t
=
C
I
A
s
h
c
d
T
d
t
=
(
1.5
)
(
12
+
0.2
t
)
(
0.15
)
125
×
100
d
T
=
(
1.5
)
(
12
+
0.2
t
)
(
0.15
)
d
t
125
×
100
T
=
∫
d
T
=
20
∫
0
(
0.15
)
(
1.5
)
(
12
+
0.2
t
)
d
t
125
×
100
T
=
(
1.5
)
(
0.15
)
125
×
100
[
12
t
+
0.2
t
2
2
]
0
20
T
=
(
1.5
)
(
0.15
)
125
×
100
[
240
+
0.1
×
400
]
T
=
0.504
×
10
−
2
m
m
T
=
5.04
µ
m
© examsnet.com
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