The value of coefficient of volume expansion of glycerin is . The fractional change in the density of glycerin for a rise of in its temperature, is [2015]

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Solution

Q.
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 [2015]

1 0.025

2 0.010

3 0.015

4 0.020

Ans.
(4)

Let $ρ_{0}$ and $ρ_{T}$ be densities of glycerin at $0 ° C$ and $T ° C$ respectively. Then,

   $ρ_{T} = ρ_{0} (1 - γ Δ T)$

where $γ$ is the coefficient of volume expansion of glycerine and $Δ T$ is rise in temperature.

   $\frac{ρ_{T}}{ρ_{0}} = 1 - γ Δ T or γ Δ T = 1 - \frac{ρ_{T}}{ρ_{0}}$

Thus,   $\frac{ρ_{0} - ρ_{T}}{ρ_{0}} = γ Δ T$

Here, $γ = 5 \times 10^{- 4} K^{- 1}$ and $Δ T = 40 ° C = 40 K$

$∴$ The fractional change in the density of glycerin

$= \frac{ρ_{0} - ρ_{T}}{ρ_{0}} = γ Δ T = (5 \times 10^{- 4} K^{- 1}) (40 K) = 0.020$

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