The apparatus shown in the figure consists of four glass column connected by horizontal sections. The height of twp central columns `B & C` are `49cm` each. The two outer columns `A & D` are open to the atmosphere . `A & C` are maintained at a temperature of `95^(@)C` while the columns `B &D` are maintained at `5^(@)C`. The height of the liquid in `A & D` measured from the base line are `52.8 cm & 51cm` respectively. Determine the coefficient of thermal expansion of the liquid.

Explanation

Applying Pascal.s law from limb A to limb D
`P_(0)+rho_(A)gh_(A)-rho_(a)gh_(B)+rho_(c)gh_(c)-rho_(o)gh_(o)=P_(0)`
and `rho_(A)=rho_(C)=rho_(2)` (say) and `rho_(B)=rho_(O)=rho_(1)` (say)
`:.rho_(2)(52.8)-rho_(1)g(49)+rho_(2)g(49)-rho_(1)g(51)=0`
or `(rho_(2))/(rho_(1))=(51+49)/(52.8+49)=100/101.8`
As density decreases with rise in temperature `rho_(2)-rho_(1)[1-gamma Deltat)`
`:.(rho_(1)[1-gamma(t_(2)-t_(1))])/(rho_(1))=100/101.8`
or `1-gamma(95-5)=100/101.8`
`implies gamma=1096xx10^(-4)//^(@)C`