A small quantity of a liquid which dows not mix with water sinks to the bottom at `20^@`C, the densities of the liquid and water being 1021 and `990 kg//m^(3)`, respectively. To what teperature must the mixture be uniformly heated in order that the liquid forms globules which just float on water ? the cubical expansion of the liquid and water over the temperature ranges is `85xx10^(-5)//K` and `45xx10^(-5)//K` respectively.

Explanation

The liquid will float on water at temperature at which both of them have the same densities.
`D_("common")=(1021)/(1+85xx10^-5Deltatheta)=(998)/(1+45xx10^-5Deltatheta)`
`implies1021(1+45xx10^-5Deltatheta)=998(1+85xx10^-5Deltatheta)`
`impliesDeltatheta=59^@Cimpliestheta_2-theta_1=59^@C`
`impliestheta_2=59+20=79^@C`