A glass vessel of volume `V_(o)` is comopleated filled with volume of the liquid will overflow? Cofficient of linear expansion of gass =`alpha` and coefficient of volume expension of the liquid =`gamma_(l)`

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))`