The apparatus shown in the figure consists of four glass columns connected by horizontal sections. The height of two central columns B and C are 49 cm each. The two outer columns A and D are open to the atmosphere. A and C are maintained at a temperature of $95^{0} C$ while the columns B and D are maintained at $5^{0} C$ . The height of the liquid in A and D measured from the base are 52.8 cm and 51 cm respectively. The coefficient of thermal volume expansion of the liquid is $N \times 10^{- 4} {({}^{0}C)}^{- 1}$ , then N = -------

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Detailed Solution

$P_{0} + h_{A} ρ_{95} g = P + h_{B} ρ_{5} g a n d P_{0} + h_{D} ρ_{5} g = P + h_{c} ρ_{95} g$

On solving the above two equations

$(h_{B} + h_{D}) ρ_{5} = (h_{A} + h_{C}) ρ_{95}$

$100 ρ_{5} = 101.8 ρ_{95} \frac{100 ρ_{0}}{1 + 5 γ} = \frac{101.8 ρ_{0}}{1 + 95 γ} 90 γ = 0.018 \Rightarrow γ = 2 \times 10^{- 4} /^{0} C$

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