The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is $n$ times the volume of the bubble $B$, then, the value of $n$ is ___.

Question

Aicharya · Accepted Answer

$\begin{aligned} & \Delta \mathrm{P}=\frac{4 \mathrm{~T}}{\mathrm{R}} \ & \frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}=\frac{\Delta \mathrm{P}_{\mathrm{B}}}{\Delta \mathrm{P}_{\mathrm{A}}}=2 \ & \frac{\mathrm{~V}_{\mathrm{A}}}{\mathrm{V}_{\mathrm{B}}}=\left(\frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}ight)^3=8\end{aligned}$

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B…

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