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

`Delta T =30^@C`
`gamma = 49 xx 10^(-5) ""^@C^(-1)`
`Delta V = gamma V Delta T`
`V. = V+Delta V = V + gamma V Delta T = V (1 + gamma Delta T)`
`= V(1 + 49 xx 10^(-5) xx 30)= 1.014 V`
As ` rho m/V`
` therefore rho. = (m)/(V.) = (m)/(1.0147 V) = 0.9855 rho `
` therefore ` Fractional change in density ` = (rho - rho.)/(rho) `
`= (rho - 0.9855 rho)/(rho) = 0.0147`