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JEE Advanced 2021 Paper 1
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© examsnet.com
Question : 19
Total: 57
A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at
0
K
. At time
t
=
0
, the temperature of the object is
200
K
. The temperature of the object becomes
100
K
at
t
=
t
1
and
50
K
at
t
=
t
2
. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio
(
t
2
/
t
1
)
is_________________.
Your Answer:
Validate
Solution:
Heat radiated
=
σ
A
T
4
=
−
m
s
d
T
d
t
So,
100
∫
200
d
T
T
4
=
∫
0
t
1
k
d
t
⇒
1
3
T
3
|
200
100
=
k
t
1
or,
1
3
(
1
100
3
−
1
200
3
)
=
k
t
1
...............(i)
Similarly,
1
3
T
3
|
200
50
=
k
t
2
⇒
1
3
(
1
50
3
−
1
200
3
)
=
k
t
2
.......(2)
Dividing eq. (ii) by (i),
t
2
t
1
=
(
200
3
−
50
3
200
3
−
100
3
)
100
3
50
3
=
9
© examsnet.com
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