Question

a glass tube of length `133cm` and of uniform cross-section is to be filled with mercury so that the volume of the unoccupied by mercury remains the same at all temperatures. If cubical coefficient for glass and mercury are respectively `0.000026//^(@)C` and `0.000182//^(@)C` , calculate the length of mercury column.

Answer 1

`(DeltaV)_(g)=(DeltaV)_(m)`
`(DeltaV)_(g)gamma_(g)Deltatheta=(V_(0))_(m)gamma_(m)Deltatheta`
`(V_(0))_(g)gamma_(g)=(V_(0))_(m)gamma_(m)`
Let `x` : length of mercury column
`l_(0)` : length of glass tube
`Al_(0)gamma_(g)=Axgamma_(m)`
`x=(gamma_(g)l_(0))/(gamma_(m))=(0.000026xx133)/(0.000182)`
`=19cm`