Question

Two vertical glass tubes filled with a liquid are connected at their lower ends by a horizontal capillary tube. One tube is surrounded by a bath containing ice and water at $0^{\circ }C$ and the other by hot water at $t^{\circ }C$. The difference in the height of the liquid in the two columns is $△h$, and the height of the column at $0^{\circ }C$ is $h_0$. Coefficient of volume expansion of the liquid is:

• A. $\frac{△h}{h_{0}t}$
• B. $\frac{2△h}{h_{0}t}$
• C. $\frac{2h_0}{△ht}$
• D. $\frac{h_0}{△ht}$

Answer 1

The correct option is A $\frac{△h}{h_{0}t}$

At equilibrium,

Pressure at $A$ $=$ Pressure at $B$

$h_0{\rho }_{0}g=(h_0+\Delta h)\frac{{\rho }_0}{1+\gamma t}g$

$h_0{\rho }_{0}g(1+\gamma t)=(h_0+\Delta h){\rho }_{0}g$

$h_0{\rho }_{0}g+h_0{\rho }_{0}g\gamma t=h_0{\rho }_{0}g+\Delta h{\rho }_{0}g$

$⟹\gamma =\frac{\Delta h}{h_{0}t}$