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. `0.0012`
B. `0.1280`
C. `0.0235`
D. `0.0145`

Answer

D

Explanation

Here, `gamma=4.9xx10^(-4)""^(@)C^(-1),DeltaT=30K=30""^(@)C`
As `V'=V+DeltaV=V(1+gammaDeltaT)`
`=V(1+4.9xx10^(-4)xx30)=10147 V`
`rArr(V')/(V)=1.0147`
Now, `p=m/VrArrVprop1/p`
`thereforep'=(p-0.9855p)/(p)=0.0145`