Question

The vertical column 50 cm long at 50 degree celsius balances another column of same liquid 60cm long at 100 degree celsius the coefficient of absolute expansion of the liquid is

Answer 1

Hii friend,

● Answer-
0.005 °C

● Explaination-
# Given-
h1 = 50 cm
h2 = 60 cm
T1 = 50 °C
T2 = 100 °C

# Solution-
Hydrostatic pressure is same for both columns coz of same liquid.
ρ1h1g = ρ2h2g
h1/h2 = ρ2/ρ1

But, ρ1 = ρ/(1+γT1) and ρ2 = ρ/(1+γT2),
h1/h2 = (1+γT1)/(1+γT2)
50/60 = (1+50γ)/(1+100γ)
50+5000γ = 60+3000γ
2000γ = 10
γ = 0.005 °C

Coefficient of absolute expansion is 0.005 °C.

Hope this is useful...

Answer 2

$\sf \dfrac{h_1}{h_2} = \dfrac{p_2}{p_1} = \dfrac{(1 + \gamma \theta _1)}{(1 + \gamma \theta _2)}$


$\sf\dfrac{50}{60} = \dfrac{1 + \gamma \times 50}{1 + \gamma \times 100}$


$\bf \gamma = 0.005°C$