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The value of coefficient of volume expansion of glycerin is $5 \times 10^{- 4} K^{- 1}$ . The fractional change in the density of glycerin for a rise of 40°C in its temperature, is

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0.025

0.010

0.015

0.020

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detailed solution

Correct option is D

Let ρ0 and ρT be densities of glycerin at 0°C and T°C respectively, then,ρT=ρ0(1-γΔT) where γ is the coefficient of volume expansion of glycerine and ∆T is rise in temperature. ρTρ0=1-γΔT or γΔT=1-ρTρ0 Thus, ρ0-ρTρ0=γΔT Here, γ=5×10-4 K-1and ΔT=40°C=40 K∴ The fractional change in the density of glycerin =ρ0-ρTρ0=γΔT=5×10-4 K-1(40 K)=0.020

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A vessel having coefficient of cubical expansion $γ_{g}$ contains liquid Of coefficient of real expansion r_R up to certain level. When Vessel
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