A glass rod weighs 90g times g in air. It weighs 49.6g times g when immersed in a liquid at 12^(@)C, and 51.9g times g at 97^(@)C. Find the real expansion coefficient of the liquid. [Volume expansion coefficientof glass =2.4 times 10^(-5@)C^(-1)]

A glass rod weighs 90g times g in air. It weighs 49.6g times g when im

1.	A glass rod weighs 90g times g in air. It weighs 49.6g times g when immersed in a liquid at 12^(@)C, and 51.9g times g at 97^(@)C. Find the real expansion coefficient of the liquid. [Volume expansion coefficientof glass =2.4 times 10^(-5@)C^(-1)]
Answer» Solution :LET the VOLUME of the glass rod be `V_(1) " at " 12 ^(@)C`, and density of the liquid be `rho_(1).` The mass of the displaced liquid at that temperature `""=90-49.6=40.4g` `THEREFORE` Volume of the glass rod at that temperature, `"" V_(1)=40.4/rho_(1) "...(1)"` Again at `97^(@)C`, mass of the displaced liquid `""=90-51.9=38.1g` Let at `97^(@)C` the volume of the glass rod be `V_(2)` and density of the liquid be `rho_(2)`. `therefore "" V_(2)=38.1/rho_(2) "...(2)"` From (1) and (2), `"" V_(2)/V_(1)=rho_(1)/rho_(2) times 38.1/40.4 "...(3)"` Now for the glass rod, `V_(2)=V_(1)[1+2.4 times 10^(-5) times 85]` `therefore"" V_(2)/V_(1)=1+2.4 times 10^(-5) times 85=1.00204` In case of liquid, `rho_(1)=rho_(2)[1+gamma times 85]` `therefore "" rho_(1)/rho_(2)=1+gamma times 85` Fromequation (3), `"" 1.00204=(1+gamma times 85) times 38.1/40.4` or, `"" 1+85gamma=(1.00204 times 40.4)/38.1` or,`""85gamma=(1.00204 times 40.4)/38.1-1=2.382/38.1` or, `"" gamma=7.35 times 10^(-4@)C^(-1).`