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Question: If the volume of a block of metal changes by 0.12%, when it is heated through 20 °C, then the coeffi...

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

A

4×10−5oC−14 \times 1{0^{- 5}}^{o}C^{- 1}

B

2×10−5oC−12 \times 1{0^{- 5}}^{o}C^{- 1}

C

12×10−5oC−1\frac{1}{2} \times 1{0^{- 5}}^{o}C^{- 1}

D

4×10−4oC−14 \times 1{0^{- 4}}^{o}C^{- 1}

Answer

2×10−5oC−12 \times 1{0^{- 5}}^{o}C^{- 1}

Explanation

Solution

Here, ΔVV=0.12%,=0.12100\frac{\Delta V}{V} = 0.12\%, = \frac{0.12}{100}

ΔT=20∘C\Delta T = 20{^\circ}C

Now, γ=ΔTVΔT=0.12100×20=6×10−5∘C−1\gamma = \frac{\Delta T}{V\Delta T} = \frac{0.12}{100 \times 20} = 6 \times 10^{- 5}{^\circ}C^{- 1}

∴α=γ3=2×10−5∘C−1.\therefore\alpha = \frac{\gamma}{3} = 2 \times 10^{- 5}{^\circ}C^{- 1}.