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

Answer

`6.7 xx 10^(5)//^(@)C`

Explanation

Pressure at the bottom of A-B limb: `P_(0) + rho_(95)gh_(1) = P_(B) + rho_(5)gh …..(i)`
Pressure at the bottom of C-D limb: `P_(B) + rho_(95) gh = P_(0) + rho_(5) xx g xx h_(2)(P_(B)-P_(C)) …(ii)`
Solving we get , `gamma = 2xx 10^(-4).^(@)C^(-1) therefore alpha = (2)/(3)xx 10^(4)"^(2)C^(-1)`