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

Explanation

`h_(A)=52.8cm` , `h_(B)=h_(C)49cm` , `h_(D)=51cm`
As the liquid is in the horizontal tube `PQ` is at rest, gauge
Pressure at `P` =gauge pressure
`p_(0)+p_(95)gh_(A)-p_(5)gh_(B)=p_(0)+p_(5)gh_(D)-p_(95)gh_(C)`
`p_(95)(h_(A)+h_(C))=p_(5)(h_(B)+h_(D))`
`(p_(5))/([1+gamma(95-5)])(52.8+49)=p_(5)(49+51)`
`1+90gamma=(101.8)/(100)=1.018`
`gamma=(0.018)/(90)=2xx10^(-4)//^(@)C`