A thin copper wire of length L increases 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?

The coefficient of linear expansion (α) is half the coefficient of superficial expansion( β).  Mathematically the equation can be expressed as, β=2α

Given:

\(\Delta T = 100 – 0 = 100^{\circ}C\) \(\Delta L/L = Length = L = 1% = 1/100 = 0.01\) \(\Delta L = \alpha x 100\) \(0.01 =\alpha x 100\) \(\alpha = 0.01 / 100 = 1 * 10^{-4}\)

Given Area of copper plate =\(2L * L = 2L^{2}\)

Accoring to thermal expansion theory,

\( \Delta A = \beta A\Delta T \) \( \Delta A / A = \beta\Delta T \)

Here\( \beta = 2\alpha \) \( \Delta A / A = 2\alpha\Delta T \)

=\( 2 * 1 * 10^{-4} * 100 \)

= \( 2 * 10^{-2} \) \( \Delta A / A * 100 \)

= \( 2 * 10^{-2} \)

= 2%

Therefore, the percentage change in the area when a thin copper plate having dimensions 2L*L is heated from T1 to T2 is 2 percentage or 2%

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