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. `0.010`
C. `0.015`
D. `0.020`

Answer

D

Explanation

Suppose the density of glycerin at temperature `0^(@)C and T^(@)C` are `rho _(0) and rho _(T)`
` therefore rho _(T) = rho )(0) [ 1- gamma Delta T], ` where `gamma=` coefficient of volume expansion and rise of temperature is `Delta T`
`therefore ( rho _(T))/( rho_(0)) =1- gamma Delta T implies gamma Delta T = 1 - (rho _(T))/( rho _(0))`
`therefore Y Delta T = (rho _(0) - rho _(T))/( rho _(0))`
`therefore 5 xx 10 ^(-4) xx 40 = (rho _(0) - rho _(T))/( rho _(0))`
`therefore ( rho _(0) - rho _(T))/( rho _(0)) = 200 xx 10 %(-4) = 0.020`