Questions
Two spherical soap bubbles in vacuum are connected through a narrow tube. Radius of left bubble is and that of right bubble is . Air flows from one side to another very slowly maintaining spherical shape of bubbles . At any instant before steady state is reached, are radius, surface area, volume and number of moles of gas in the left bubble and are radius, surface area, volume and number of moles in the right bubble. Assume that temperature T remains constant throughout the process. Let initially and S be the surface tension of soap solution. Choose the correct option(s). (R is universal gas constant)
detailed solution
Correct option is C
At any instant the total number of moles n1+n2=n remains constant Also, n1n2=P1V1P2V2=4Sr1×43πr134Sr2×43πr23=r1r22=14∴n1+n2=2+8=10=constantP1V1+P2V2=nRT⇒4Sr1×43πr13+4Sr2×43πr23=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⇒4πR02+4π4R02 =4πr12+4πr22⇒r12+r22=R02+4R02=5R02∴r12=110×5R02⇒r1=R02⇒r2=3R02Talk to our academic expert!
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