two vessels made of different metals are similar in shape and size they are fully filled with ice at 0c by the heat from outside all the ice. in one vessel melts in 25 minutes and that in other vessel in 20minutes campare their conjunctivitis
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Let the vessel be cubic of side a and thickness be d
t
1
=10min
t
2
=25min
Let the room temperature be T
o
Thermal conductivity of the first and the second vessel be K
1
and K
2
respectively.
Let △Q amount of heat is required to melt volume of ice; △Q=
d
6K
1
a
2
(T
o
−0)t
1
( factor of 6 is for 6 sides of cube through which heat is flowing in)
⇒△Q
1
=
d
6K
1
a
2
(T
o
−0)10
For second container, △Q
2
=
d
6K
2
a
2
(T
o
−0)25
∵△Q
1
=△Q
2
⇒
d
6K
1
a
2
(T
o
−0)10
=
d
6K
2
a
2
(T
o
−0)25
⇒10K
1
=25K
2
⇒K
1
:K
2
=25:10=5:2
⇒K
1
:K
2
=5:2
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