Question

A vertical column 50 cm long at 50°C balances another column of same liquid 60 cm long at 100°C. The coefficient of absolute expansion of the liquid is

• A. (a) 0.005/°C
• A. (b) 0.0005/°C
• A. (c) 0.002/°C
• A. (d) 0.0002/°C

Answer 1

(a)

Sol. $\frac{h_{1}}{h_{2}} = \frac{\rho_{1}}{\rho_{2}} = \frac{(1 + \gamma\theta_{1})}{(1 + \gamma\theta_{2})}$ $\left\lbrack \because\rho = \frac{\rho_{0}}{(1 + \gamma\theta)} \right\rbrack$

⇒ $\frac{50}{60} = \frac{1 + \gamma \times 50}{1 + \gamma \times 100}$ ⇒ $\gamma = 0.005/{^\circ}C$