A glass vessel measures exactly 10cm xx 10 cm xx 10 cm at `0^@C`. It is filled completely with mercury at this temperature. When the temperature is raised to `10^@C`, `1.6cm^3` of mercury overflows. Calculate the coefficient of volume expansion of mercury. coefficient of linear expansion of glass `= 6.5 xx 10^(-6)C^(-1)`.

Explanation

Given,
`V_g =10 xx 10 xx 10= 1000 cc.`
`Delta T = 10^@C`
`V'_Hg - V'_g =1.6 cm^3`
`alpha_g = 6.5 xx 10^-6/^@C`
`gamma_Hg =?`
`gamma_g =(3 xx 6.5 xx 10^-6/^@C)`
`V'_Hg = V_Hg(1+(gamma_Hg) Delta T) …….(1)`
`V'_g = V_g(1+ (gamma_g) Delta T) .........(2)`
` (V'_Hg - V'_g) =( V_Hg - V_g +(V_Hg (gamma_Hg) Delta T`))
` (-V_g (gamma_g) Delta T )`
` 1.6= (1000 xx (gamma_Hg) xx 10 - 1000)`
`(xx 6.5 xx 3 xx 10^-6 xx 10)`
` gamma_Hg =((1.6+ 19.5 xx 10^-2)/10000)` = 1.795/ 10000`
`=1.795 xx 10^-4 `
`1.8 xx (10^-4/^@C)`