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Question: Density of substance at 0°C is 10 gm/cc and at 100°C, its density is 9.7 gm/cc. The coefficient of l...

Density of substance at 0°C is 10 gm/cc and at 100°C, its density is 9.7 gm/cc. The coefficient of linear expansion of the substance will be

A

102

B

10–2

C

10–3

D

10–4

Answer

10–4

Explanation

Solution

Coefficient of volume expansion

γ=Δρρ.ΔT=(ρ1−ρ2)ρ.(Δθ)=(10−9.7)10×(100−0)=3×10−4\gamma = \frac{\Delta\rho}{\rho.\Delta T} = \frac{(\rho_{1} - \rho_{2})}{\rho.(\Delta\theta)} = \frac{(10 - 9.7)}{10 \times (100 - 0)} = 3 \times 10^{- 4}

Hence, coefficient of linear expansion

α=γ3=10−4/∘C\alpha = \frac{\gamma}{3} = 10^{- 4}/{^\circ}C