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

Suppose final density is `d_f` and initial density is `d_i`.
`therefore d_f=(di)/(1+gammaDeltaT)rArr d_i/d_f =(1-gammaDeltaT)`…(1)
Fractional change in density =`(d_i-d_f)/d_i`
`=1-d_f/d_i`
`=1-(1-gamma DeltaT)^(-1)`
Using binomial theorem for expansion from equation (1),
`=1-(1-gammaDeltaT)`
`=gamma DeltaT`
`=5xx10^(-4)xx40`
`=2xx10^(-2)`
=0.020