The coefficient of volume expansion of glycerine is `49 xx 10^(-5)//^(@)C`. What is the fractional change in its density (approx.) for `30^(@)C` rise in temperature?

Explanation

Here, `gamma = 49xx10^(-5) .^@C^(-1), Delta T = 30^@C.`
As m`V' = V + Delta V = (V(1+gamma Delta t) :. V'= V(1+49 xx 10^(-5)xx30) = 1.0147 V`
As, `rho = (m)/(V), rho' = (m)/(V') = (m)/(1.0147 V) = 0.9855 rho`
Fractional change in density ` = (rho - rho')/(rho) = (rho - 0.9855 rho)/(rho) = 1.0145`