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Question

A thin copper wire of length L increases in length by 1% when heated from temperature T1 to T2. What is the percentage change in area when a thin copper plate having dimensions 2L×L is heated from T1 to T2?

A
1%
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B
2%
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C
3%
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D
4%
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Solution

The correct option is B 2%
Given:
ΔT=1000=100°C
ΔL/L=length=L=1%=1/100=0.01
ΔL=αLΔT
ΔL/L=α×100
0.01=α×100
α=0.01/100=1×104
Given Area of copper plate =2L×L=2L2
By thermal expansion theory,
ΔA=βAΔT
ΔA/A=βΔT
but,
β=2α
ΔA/A=2αΔT
=2×1×104×100
=2×102
ΔA/A×100=2×102×100=2%
Hence,
option (B) is correct answer.

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