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. `0.010`
B. `0.015`
C. `0.020`
D. `0.025`

Answer

C

Explanation

Here, `gamma=5xx10^(-4)K^(-1)= 5xx10^(-4).^(@)C^(-1)`
Let, `rho_(2), rho_(1)` be the density of glycerine at temperature `t_(2).^(@)C` and `t_(1).^(@)C` respectively. Then
`rho_(2)=rho_(1)[1-gamma(t_(2)-t_(1))]=rho_(1)-rho_(1)(t_(2)-t_(1))`
or `(rho_(1)-rho_(2))/(rho_(1))=gamma(t_(2)-t_(1))`
Frictional change in density of glycerine
`=(rho_(1)-rho_(2))/(rho_(1))= gamma(t_(2)-t_(1))= (5xx10^(-4))xx40`
`=0.020`