The value of coefficient of volume expansion of glycerin is `5xx10^(4)K^(-1)` . The fractional change in 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 glycerin 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)gamma(t_(2)-t_(1)`
or `(rho_(1)-rho_(2))/(rho_(1))=gamma(t_(2)-t_(1))`
Fractional change in the density of glycerine
`(rho_(1)-rho_(2))/(rho_(1)) =gamma(t_(2)-t_(1)) =(5xx10^(-4))xx40`
`=0.020`