MHT CET · Physics · Thermodynamics
The radii of two soap bubbles are \(r_1\) and \(r_2\). In isothermal condition they combine with each other to form a single bubble. The radius of resultant bubble is
- A \(\mathrm{R}=\frac{\mathrm{r}_1+\mathrm{r}_2}{2}\)
- B \(R=r_1\left(r_1 r_2+r_2\right)\)
- C \(\mathrm{R}=\sqrt{\mathrm{r}_1^2+\mathrm{r}_2^2}\)
- D \(\mathrm{R}=\mathrm{r}_1+\mathrm{r}_2\)
Answer & Solution
Correct Answer
(C) \(\mathrm{R}=\sqrt{\mathrm{r}_1^2+\mathrm{r}_2^2}\)
Step-by-step Solution
Detailed explanation
Under isothermal condition, \(\mathrm{T}\) is constant.
This means the surface energy of the bubbles before combining will be equal to the surface energy after combining.
\(\begin{aligned}
& \quad \text { i.e. } 4 \pi r_1^2 T+4 \pi r_2^2 T=4 \pi R^2 T \\
& \Rightarrow r_1^2+r_2^2=R^2 \\
& \therefore \quad R=\sqrt{r_1^2+r_2^2}
\end{aligned}\)
This means the surface energy of the bubbles before combining will be equal to the surface energy after combining.
\(\begin{aligned}
& \quad \text { i.e. } 4 \pi r_1^2 T+4 \pi r_2^2 T=4 \pi R^2 T \\
& \Rightarrow r_1^2+r_2^2=R^2 \\
& \therefore \quad R=\sqrt{r_1^2+r_2^2}
\end{aligned}\)
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