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Question: The volume of a metal sphere increases by 0.24% when its temperature is raised by 40°C. The coeffici...

The volume of a metal sphere increases by 0.24% when its temperature is raised by 40°C. The coefficient of linear expansion of the metal is

A

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

B

6×10−5oC−16 \times 1{0^{- 5}}^{o}C^{- 1}

C

18×10−5oC−118 \times 1{0^{- 5}}^{o}C^{- 1}

D

1.2×10−5oC−11.2 \times 1{0^{- 5}}^{o}C^{- 1}

Answer

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

Explanation

Solution

From, Vr=V0(1+γΔT)⇒Vr−V0V0=γΔTV_{r} = V_{0}(1 + \gamma\Delta T) \Rightarrow \frac{V_{r} - V_{0}}{V_{0}} = \gamma\Delta T

0.24100=γ40∘C\frac{0.24}{100} = \gamma 40{^\circ}C

γ=0.24100×40=6×10−5∘C−1\gamma = \frac{0.24}{100 \times 40} = 6 \times 10^{- 5}{^\circ}C^{- 1}

Coefficient of linear expansion,

α=γ3−6×10−53=2×10−5∘C−1\alpha = \frac{\gamma}{3} - \frac{6 \times 10^{- 5}}{3} = 2 \times 10^{- 5}{^\circ}C^{- 1}