The value of coefficient of volume expansion of glycerin is `5 xx 10^(-4) K^(-1)`. The fractional change in the density of glycerin for a rise of `40^(@)C` in its temperature is

Options

A. 0.025
B. 0.01
C. 0.015
D. 0.02

Answer

D

Explanation

Let `rho_(0) and rho_(7)` be densities of glycerin at `0^(@)C and 7^(@)C` respectively. Then, `rho_(T) = rho_(0) (1- gamma Delta T)` where `gamma` is the coefficient of volume expansion of glycerine and `Delta T` is rise in temperature.
`(rho_(T))/(rho_(0)) = 1- gamma Delta T or gamma Delta T= 1 - (rho_(T))/(rho_(0))`
Thus, `(rho_(0) - rho_(T))/(rho_(0)) = gamma Delta T`
here, `gamma = 5 xx 10^(-4) K^(-1) and Delta T= 40^(20C = 40K`
`:.` The fractional change in the density of glycerin `= (rho_(0)- rho_(T))/(rho_(0)) = gamma Delta T = (5 xx 10^(-4) K^(-1)) (40K) = 0.020`