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Question

One end of a copper rod of uniform cross section and length 1.5 m is in contact with ice and the other end with steam at 100C. At what point along its length from A should a temperature of 200C be maintained so that in steady state, the mass of the ice melting is equal to that of steam produced in the same interval of time . [Lv=540 cal/g,Lf=80 cal/ g]


A
10.34 cm
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B
9.1 cm
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C
20 cm
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D
5 cm
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Solution

The correct option is A 10.34 cm
Let C be the point where 200C temperature is maintained.


Heat flow towards the end A is given by
H1=kA(200100)x=m×540 .....(1)
where m is rate of steam produced.
Heat flow towards the end B is given by
H2=kA(2000)150x=m×80 ....(2)
where m is rate of ice melting.

Given m=m
By dividing (1) and (2), we get
100(150x)200x=54080
8(150x)=54×2x
116x=1200
x=10.34 cm
Thus, option (a) is the correct answer.

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