The coefficient of volume expansion of glycerin is `49xx10^(-5)K^(-1)`. What is the fractional change in its density for a `30^(@)C` rise in temperature ?

Explanation

IF volume glycerine becomes V with increase in temperature by `30^(@)C`, then
`V=V_(0)(1+gammaDeltaT)`
But `V=(M)/(rho)` and `V_(0)=(M)/(rho_(0))`,
`:.(M)/(rho)=(M)/(rho_(0))(1+gammaDeltaT)`
`:.(rho)/(rho_(0))=1/((1+gammaDeltaT))`
`:.(rho-rho_(0))/(rho_(0))=(1-1-gammaDeltaT)/(1+gammaDeltaT)`
`:.(rho-rho_(0))/(rho_(0))=(-gammaDeltaT)/(1+gammaDeltaT)`
`=(-49xx10^(-5)xx30)/(1+49xx10^(-5)xx30)`
`(Delta rho)/(rho_(0))=-0.0145`
Negative sign represents the decrease in density
`=0.0145~~1.5xx10^(-2)`