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

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

Grade:11

2 Answers

Arun
25763 Points
3 years ago
Dear Preeti
 
See, suppose we have l* as the initial length and l being the final length 
Hence, l=l* x (1+αΔt); 
where Δt= t2-t1 and α=coefficient of linear expansion 
or, l=l* + l* x αΔt 
or, (l-l*)/l*=αΔt=1/100
So, A=A* x (1+βΔt); //b=coefficient of area expansion 
or (A-A*)/A* 
=βΔt 
=2αΔt=2/100=2% (β=2α)
 
Regards
Arun (askIITians forum expert)
Rishi Sharma
askIITians Faculty 646 Points
11 months ago
Dear Student,
Please find below the solution to your problem.

Suppose we have l* as the initial length and l being the final length
Hence, l=l* x (1+αΔt);
where Δt= t2-t1 and α=coefficient of linear expansion
or, l=l* + l* x αΔt
or, (l-l*)/l*=αΔt=1/100
So, A=A* x (1+βΔt); //b=coefficient of area expansion
or (A-A*)/A*
=βΔt
=2αΔt=2/100=2% (β=2α)

Thanks and Regards

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