Question

The radii of two soap bubbles are R₁ and R₂ respectively. The ratio of masses of air in them will be

• A. $\frac{R_{1}^{3}}{R_{2}^{3}}$
• B. $\frac{R_{2}^{3}}{R_{1}^{3}}$
• C. $\left( \frac{\mathbf{P +}\frac{\mathbf{4T}}{\mathbf{R}_{\mathbf{1}}}}{\mathbf{P +}\frac{\mathbf{4T}}{\mathbf{R}_{\mathbf{2}}}} \right)\frac{\mathbf{R}_{\mathbf{1}}^{\mathbf{3}}}{\mathbf{R}_{\mathbf{2}}^{\mathbf{3}}}$
• D. $\left( \frac{P + \frac{4T}{R_{2}}}{P + \frac{4T}{R_{1}}} \right)\frac{R_{2}^{3}}{R_{1}^{3}}$

Answer 1

Answer: (C)

$\left( \frac{\mathbf{P +}\frac{\mathbf{4T}}{\mathbf{R}_{\mathbf{1}}}}{\mathbf{P +}\frac{\mathbf{4T}}{\mathbf{R}_{\mathbf{2}}}} \right)\frac{\mathbf{R}_{\mathbf{1}}^{\mathbf{3}}}{\mathbf{R}_{\mathbf{2}}^{\mathbf{3}}}$

Answer 2

From PV = μRT.

At a given temperature, the ratio masses of air $\frac{\mu_{1}}{\mu_{2}} = \frac{P_{1}V_{1}}{P_{2}V_{2}} = \frac{\left( P + \frac{4T}{R_{1}} \right)}{\left( P + \frac{4T}{R_{2}} \right)}\frac{\frac{4}{3}\pi R_{1}^{3}}{\frac{4}{3}\pi R_{2}^{3}} = \frac{\left( P + \frac{4T}{R_{1}} \right)}{\left( P + \frac{4T}{R_{2}} \right)}\frac{R_{1}^{3}}{R_{2}^{3}}.$