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Question

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


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Solution

Step 1: Given

Length of the copper wire = L

Percentage change in the length, LL=1%=1100=0.01

Initial temperature = T1

Final temperature = T2

Dimension of copper plate = 2L×L

Assume the coefficient of linear expansion be α.

Assume the coefficient of area (superficial) expansion be β.

Step 2: Formula used and calculation

We know that

LL=αT0.01=α(T2-T1)-----(1)

Area of copper plate = 2L×L

On heating change in the area will be given by

A=βATAA=βT

We know that for a given material β=2α.

Therefore,

AA=βTAA=2αTAA=2α(T2-T1)AA=2×0.01(Fromeq(1))AA=0.02

Therefore change in area will be 2%.


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