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Question

A thin brass sheet at 10C and a thin steel sheet at 20C have same surface area. The common temperature at which both would have the same area is :
Coefficient of areal expension for brass and steel are 10×106C1 and 20×106C1 respectively.

A
10C
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B
20C
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C
30C
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D
35C
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Solution

The correct option is C 30C
We know ,
Final area A=A0(1+βΔT)
where A0 is initial area.

Given:
A0 is same for both brass and steel sheet at 10C and 20C respectively.
Let at temperature T, both have same area A.
A0(1+βbΔT1)=A0(1+βsΔT2)
A0(1+βb(T10))=A0(1+βs(T20))
βbβs=T20T10
10×106C120×106C1=T20T10
T=30C

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