The apparatus shown in the figure consists of four glass columns connected by horizontal sections. The height of two central columns B & C are 49 cm each. The two outer columns A & D are open to the atmosphere. A & C are maintained at a temperature of 95º C while the columns B & D are maintained at 5º C. The height of the liquid in A & D measured from the base line are 52.8 cm & 51 cm respectively. Determine the coefficient of thermal expansion of the liquid.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Density of a liquid varies with temperature as–
= 
Here γ is the coefficient of volume expansion of liquid.
In the figure –
h 1 = 52.8 cm, h 2 = 51 cm and h = 49 cm
Now pressure at B = pressure at C.
Therefore , –
P 0 + h 1 
g - h 
g = P 0 + h 2 
g – h 
g
⇒ 
(h 1 + h) = 
(h 2 + h)
⇒ 
= 
⇒ 
= 
⇒ 
= 
= 
Solving this equation, we get
γ = 2 × 10 -4 per ºC
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