First slide

Thermal expansion

Question

If the volume of a block of metal changes by 0.12%. when it is heated through 20°C, then the coefficient of linear expansion is

Moderate

A

$4 \times {10^{- 5}}^{\circ} C^{- 1}$
B

$2 \times {10^{- 5}}^{\circ} C^{- 1}$
C

$0.5 \times {10^{- 5}}^{\circ} C^{- 1}$
D

$4 \times {10^{- 4}}^{\circ} C^{- 1}$

Solution

Here, $\frac{ΔV}{V} = 0 .12 %, = \frac{0 .12}{100}$
$Δ T = 20^{\circ} C$
Now, $γ = \frac{ΔV}{VΔT} = \frac{0 .12}{100 \times 20} = 6 \times {10^{- 5}}^{\circ} C^{- 1}$
$∴ α = \frac{γ}{3} = 2 \times {10^{- 5}}^{\circ} C^{- 1} .$

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