Question

A long mercury glass tube with a uniform capillary bore has in it a thread of mercury which is `1m` long at `0^(@)C` . What will be its length at `100^(@)C` if the real coefficient of expansion of mercury is `0.000182` and coefficient of cubical expansion of glass equal to `0.000025` ?

Answer 1

`V_(0)` , volume of mercury thread at `0^(@)C`
`V_(theta)` : volume of mercury thread at `theta^(@)C`
`A_(0)` : cross-sectional area of tube at `0^(@)C`
`A_(theta)` : cross-sectional area of tube `theta^(@)C`
The length of thread at `theta^(@)C`
`l_(theta)=V_(theta)/(A_(theta))=(V_(0)(1+gamma_(m)theta))/(A_(0)(1+betatheta)`
`=l_(0)(1+gamma_(m)theta)(1+betatheta)^(-1)`
`=l_(0)(1+gamma_(m)theta)(1+betatheta)`
`=l_(0)[1+(gamma_(m)-beta)theta]["Neglectting small terms"]`
`=l_(0)[1+(gamma_(m)-(2gamma_(g))/(3))theta]`
`=100[1+(0.000182-(2)/(3)xx0.000025)xx100]`
`=101.654cm`