Heat and Thermodynamics 2 Question 8

11. The apparatus shown in figure consists of four glass columns connected by horizontal sections. The height of two central columns B and C are 49cm each. The two outer columns A and D are open to the atmosphere.

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Solution:

  1. Density of a liquid varies with temperature as

ρtC=(ρ0C1+γt)

Here, γ is the coefficient of volume expansion of temperature.

In the figure

h1=52.8cm,h2=51cm and h=49cm

Now, pressure at B= pressure at C

p0+h1ρ95ghρ5g=p0+h2ρ5ghρ95gρ95(h1+h)=ρ5(h2+h)ρ95ρ5=h2+hh1+hρ01+95γρ01+5γ=h2+hh1+h

1+5γ1+95γ=51+4952.8+49=100101.8

Solving this equation, we get

γ=2×104/C

Coefficient of linear expansion of temperature,

α=γ3=6.7×105/C



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