112 question solution please

​Q112. Two soap bubbles 'A' and 'B' are kept in a closed chamber where the air is maintained at pressure 8 N/m2. The radii of bubbles 'A' and 'B' are 2 cm and 4 cm respectively. Surface tension of the soap water used to make bubbles is 0.04 N/m. The ratio of number of moles of air in bubble 'A' to that in bubble 'B' is

      (1) 4 :3

      (2) 9 : 4

      (3) 8 : 3

      (4) 1: 6
 

Dear Student,

Because for soap bubble there will be pressure difference due surface tensionΔP=4TRPin-Pout=4TR         Pin=Pout+4TRLet inside pressure for soap bubbles are P1 and P2P1=Pout+4TR1=8 +4×0.042×10-2=16 Nm-2P2=Pout+4TR2=8 +4×0.044×10-2=12 Nm-2For ideal gas  ,       PV=n RTn=PVRT       n α P r 3  (here r is radius of soap bubble)n1n2=P1P2r1r23    n1n2=1612243 =16 n1 :n2 =1 : 6 
Regards.

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