Two spherical soap bubbles in vacuum are connected through a narrow tube. Radius of left bubble is $$R0$$ and that of right bubble is $$2R0$$. Air flows from one side to another very slowly maintaining spherical shape of bubbles . At any instant before steady state is reached, $$r1$$, $$A1$$, $$V1$$, $$n1$$ are radius, surface area, volume and number of moles of gas in the left bubble and $$r2$$, $$A2$$, $$V2$$, $$n2$$ are radius, surface area, volume and number of moles in the right bubble. Assume that temperature T remains constant throughout the process. Let $$n1=2$$ initially and S be the surface tension of soap solution. Choose the correct $$option(s)$$. (R$$ is universal gas $$constant)

Question

Two spherical soap bubbles in vacuum are connected through a narrow tube. Radius of left bubble is $$R0$$  and that of right bubble is $$2R0$$. Air flows from one side to another very slowly maintaining spherical shape of bubbles . At any instant before steady state is reached,  $$r1$$,  $$A1$$,  $$V1$$,  $$n1$$ are radius, surface area, volume and number of moles of gas in the left bubble and  $$r2$$,  $$A2$$,  $$V2$$,  $$n2$$ are radius, surface area, volume and number of moles in the right bubble. Assume that temperature T remains constant throughout the process. Let  $$n1=2$$ initially and S be the surface tension of soap solution. Choose the correct $$option(s)$$. (R$$ is universal gas $$constant)

Infinity Learn · Accepted Answer

At any instant the total number of moles  $$n1+n2=n$$ remains constant Also, $$n1n2=P1V1P2V2=4Sr1$$×$$43$$$$π$$$$r134Sr2$$×$$43$$$$π$$$$r23=r1r22=14$$∴$$n1+n2=2+8=10=constantP1V1+P2V2=nRT$$⇒$$4Sr1$$×$$43$$$$π$$$$r13+4Sr2$$×$$43$$$$π$$$$r23=10RT$$⇒$$A1+A2=7.5RTS=Total$$ Surface Area is constant When, $$n1=1$$⇒$$n2=9$$∴$$r1r22=19$$⇒$$r2=3r1$$; Also, since, total surface area is constant Initial surface $$area=Final$$ surface area⇒$$4$$$$π$$$$R02+4$$$$π$$$$4R02$$ $$=4$$$$π$$$$r12+4$$$$π$$$$r22$$⇒$$r12+r22=R02+4R02=5R02$$∴$$r12=110$$×$$5R02$$⇒$$r1=R02$$⇒$$r2=3R02$$

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