Question

An air bubbles starts rising from the bottom of a lake. Its diameter is 3.6 mm at the bottom and 4mm at the surface. The depth of the lake is 2.5m and the temperature at the surface is 40 ${}^{0}C$ then temperature at the bottom is :

• A. 25${}^0$C
• B. 20${}^0$C
• C. 15${}^0$C
• D. 12${}^0$C

Answer 1

The correct option is D 12${}^0$C

The air inside the bubble must follow the Ideal Gas Equation.

Hence $\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

$⟹\frac{(P_0+\rho g(2.5\left)\right)\times \frac{4}{3}\pi r_1^3}{T_2}=\frac{P_0\times \frac{4}{3}\pi r_2^3}{313}$

$⟹T_2=285K={12}^{\circ }C$