A glass vessel of volume `100 cm^(3)` is filled with mercury and is heated from `25^(@)C to 75^(@)C`. What volume of mercury will overflow? Coefficient of linear expansion of glass `= 1.8 xx 10^(-6)//'^(@)C` and coefficient of volume expansion of mercury is `1.8 xx 10^(-4)//'^(@)C`.

Options

A. `2V_(o)AT(gamma_(l)-3alpha_(g))`
B. `V_(o)DeltaT(gamma_(l)-3alpha_(g))`
C. `V_(o)DeltaT(gamma_(l)-alpha_(g))`
D. `(V_(o)DeltaT)/2(gamma_(l)-3alpha_(g))`

Answer

B

Explanation

Volume of the liquid overflow
= Increase in the volume of the liquid
-Increase in the volume of the container
`=[V_(o)(1+gamma_(t)DeltaT)-V_(o)]-[V_(o)(1+gamma_(g)DeltaT)-V_(o)]`
`=V_(o)DeltaT(gamma_(l)-gamma_(g))=V_(o)DeltaY(gamma_(l)-3alpha_(g))" "(therefore gamma_(g)~~ 3alpha_(g))`