Question

A 1-L flask contains some mercury. It is found that at different temperature, the volume of air inside the flask remains the same. What is the volume of mercury in the flask, given that the coefficient of linear expansion of glass`=9xx10^(-6)//^(@)C` and the coefficient of volume expansion of `Hg=1.8xx10^(-4)//^(@)C` ?

Answer 1

For glass `gamma_(g) = 3 alpha_(g) = 3 xx 9 xx 10^(-6)`
` = 27 xx 10^(-6) .^(@)C^(-1)`
Volume of air in the flask, ` V =1 litre = 1000 cm^(3)`
Let `V_(m)` be the volume of mercury in the flask and `V_(a)` be the volume of air in the flask.
Volume of gas flask = volume of mercury + volume of air
`V =V_(m) + V+(a)`
As `V_(a) ` remains constant, when temperature is raised by `Delta T` , so
` Delta V = Delta V_(m)`
or, `V gamma_(g) Delta T = V_(m) gamma_(m) DeltaT`
` or V_(m) = (gamma_(g)V)/(gamma_m) = ((27 xx 10^(-6)) xx 1000)/(1.8 xx 10^(-4)) = 150 cm^(3)`.