What is the ratio of the number of moles of a | vedclass

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(C) The ideal gas equation is $PV = \mu RT$,where $\mu$ is the number of moles.For a soap bubble,the excess pressure inside is $\Delta P = \frac{4T}{R

Vedclass · Accepted Answer

$\left( \frac{P + \frac{4T}{R_1}}{P + \frac{4T}{R_2}} \right) \frac{R_1^3}{R_2^3}$

Vedclass · Answer

(C) The ideal gas equation is $PV = \mu RT$,where $\mu$ is the number of moles.For a soap bubble,the excess pressure inside is $\Delta P = \frac{4T}{R}$,so the total pressure is $P_{in} = P + \frac{4T}{R}$,where $P$ is the atmospheric pressure and $T$ is the surface tension.The volume of a spherical bubble is $V = \frac{4}{3}\pi R^3$.Thus,the number of moles $\mu$ is given by $\mu = \frac{P_{in} V}{RT} = \frac{(P + \frac{4T}{R}) \cdot \frac{4}{3}\pi R^3}{RT}$.For two bubbles with radii $R_1$ and $R_2$,the ratio of the number of moles $\frac{\mu_1}{\mu_2}$ is:$\frac{\mu_1}{\mu_2} = \frac{(P + \frac{4T}{R_1}) \cdot \frac{4}{3}\pi R_1^3}{(P + \frac{4T}{R_2}) \cdot \frac{4}{3}\pi R_2^3} = \left( \frac{P + \frac{4T}{R_1}}{P + \frac{4T}{R_2}} \right) \frac{R_1^3}{R_2^3}$.

Column-$I$	Column-$II$
$(a)$ Liquid drop in air	$(i)$ $\frac{4T}{R}$
$(b)$ Bubble of liquid in air	$(ii)$ $\frac{2T}{R}$
	$(iii)$ $\frac{2R}{T}$

What is the ratio of the number of moles of air in two soap bubbles of radii $R_1$ and $R_2$?

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$Assertion :$ $A$ bubble comes from the bottom of a lake to the top.
$Reason :$ Its radius increases.

Formation of bubbles is in Column-$I$ and the pressure difference between them is given in Column-$II$. Match them appropriately.

Column-$I$ Column-$II$

$(a)$ Liquid drop in air $(i)$ $\frac{4T}{R}$

$(b)$ Bubble of liquid in air $(ii)$ $\frac{2T}{R}$

$(iii)$ $\frac{2R}{T}$

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