First slide

Thermal expansion

Question

A thin copper wire of length L expands in length by 0.2% when it is heated from $0^{0} {C to 50}^{0} C.$ If a copper plate of area $2 L \times \frac{L}{4}$ is heated from $0^{0} {C to 100}^{0} C.$ The % increase in its area is

Moderate

A

0.2 %
B

0.4 %
C

0.8 %
D

1 %

Solution

$\begin{array}{l} α Δ t_{1} = \frac{Δ l}{l} \\ \frac{Δ A}{A} = 2 α Δ t_{2} = 4 α Δ t_{1} \\ \frac{Δ A}{A} \times 100 = 4 \times \frac{Δ l}{l} \times 100 \Rightarrow 4 \times 0.2 = 0.8 % \end{array}$

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