A solid at 0^(@)C floats with 98% of its volume immersed in a liquid. The solid floats completely immersed when the temperature is raised to 25^(@)C. If the coefficientof volume expansion of the solid is 2.6 times 10^(-6@)C^(-1), find the coefficient of real expansion of the liquid .

A solid at 0^(@)C floats with 98% of its volume immersed in a liquid.

1.	A solid at 0^(@)C floats with 98% of its volume immersed in a liquid. The solid floats completely immersed when the temperature is raised to 25^(@)C. If the coefficientof volume expansion of the solid is 2.6 times 10^(-6@)C^(-1), find the coefficient of real expansion of the liquid .
Answer» Solution :LET at `0^(@)C`, volume of the SOLID `=V_(0)`, density of the liquid `=rho_(0)`, at `25^(@)C`, volume of the solid `=V^(.)` and density of the liquid `=rho^(.)` Now, `V^(.)=V_(0)[1+2.6 times 10^(-6) times 25]` and `rho_(0)=rho^(.)[1+GAMMA times 25]` where `gamma=` coefficient of real expansion of the liquid. From the condition of floatation, `""V_(0) times 0.98 times rho_(0)=V^(.)rho^(.)` or, `""V_(0) times 0.98 times rho^(.)[1+gammatimes 25]=V_(0)[1+2.6 times 10^(-6) times 25] times rho^(.)` or, `"" 1+25 gamma=(1+0.000065)/(0.98) " or, " 25 gamma=1.02047-1` `therefore "" gamma=8.19 times 10^(-4@)C^(-1).`