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Two spherical soap bubbles of radii $a$ and $b$ in vacuum coaleasce under isothermal conditions. The resulting bubbles has a radius given by
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Verified Answer
The correct answer is:
$\sqrt{a^2+b^2}$
Since the bubbles coalesce in vacuum and there is no change in temperature, hence its surface energy does not change. This means that the surface area remains unchanged. Hence
$$
4 \pi a^2+4 \pi b^2=4 \pi R^2 \text { or } R=\sqrt{a^2+b^2}
$$
$$
4 \pi a^2+4 \pi b^2=4 \pi R^2 \text { or } R=\sqrt{a^2+b^2}
$$
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