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Question

Two rods P and Q of same length and same diameter having thermal conductivity ratio 2 : 3 joined end to end. If temperature at one end of P is 100C and at one and of Q 0C, then the temperature of the interface is

A
40C
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B
50C
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C
60C
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D
70C
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Solution

The correct option is A 40C
Let the temperature of interface of both the rod is T.
So heat flow rate will be: Qt=KAΔTL
So heat will flow from higher temperature to lower, hence at steady state we equate both of them to find the common intermediate temperature T.
Kp(100T)L=Kq(T0)L
It is given that: KpKq=23

So, on putting in above equation we find:
23(100T)=T
T=400C

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