Question

A glass flask of volume one litre at $0^{o}C$ is filled level full of mercury at this temperature. The flask and mercury is now heated to ${100}^{o}C$. How much mercury will spill if coefficient of volume expansion of mercury is $1.82\times {10}^{-4}/C^o$ and linear expansion of glass is $0.1\times {10}^{-4}/C^o$ respectively?

Answer 1

$△T={100}^{o}C$

Coefficient of Volume expansion of Mercury $=1.82\times {10}^{-4}/C^o$

Coefficient of linear expansion of glass $=0.1\times {10}^{-4}/C^o$

Now,

Overflow volume of mercury relative to flask is given by

$△V=V_o({\gamma }_m-{\gamma }_F)△T$

where, $V_o=$ initial volume of mercury, ${\gamma }_m=$ cubical constant of mercury, ${\gamma }_F=$ cubical constant of Flask

${\gamma }_F=3\times \alpha =0.3\times {10}^{-4}/C^o{V}_o=1lSo,△V=1(1.82\times {10}^{-4}-0.3\times {10}^{-4})100=1.52\times {10}^{-2}△V=0.0152litre$