First slide

Thermal expansion

Question

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

Easy

A

0.025
B

0.010
C

0.015
D

0.020

Solution

$Let ρ_{0} and ρ_{T} be densities of glycerin at 0 ° C and T ° C$ respectively, then,
$ρ_{T} = ρ_{0} (1 - γ Δ T)$
$where γ is the coefficient of volume expansion of glycerine$
and $∆ T$ 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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