The soap bubbles of radii \( r_{1} \) and \( r_{2} \) coalesce to f...
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0The soap bubbles of radii \( r_{1} \) and \( r_{2} \) coalesce to form a single bubble of radius \( r \). If the external pressure is \( P \), show that the surface tension \( T \) is given by
\[
T=\frac{P\left(r^{3}-r_{1}^{3}-r_{2}^{3}\right)}{4\left(r_{1}^{2}+r_{2}^{2}-r^{2}\right)}
\]
\( \mathrm{P} \)
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