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A vessel filled with air under pressure P° contains a soap bubble of diameter d.The air pressure have been reduced n fold and the bubble diameter increased r fold isothermally.Find the surface tension of soap water solution.(Courtesy :Cengage Physics)

Asked by Vidushi412 30th November 2018, 10:43 AM
Answered by Expert
Let P0 be the pressure in the vessel and P1 is the initial pressure inside bubble of radius d.
Then we have P1 - P0 = begin mathsize 12px style fraction numerator 8 T over denominator d end fraction end style .....................(1)
where T is surface tension
when Pressure in the vessel is reduced by n fold, bubble diameter is increased by r fold.
Under isothermal condition, if V1 was initial volume and is changed r3 times now, then pressure reduced by r3 times (PV is constant)
Hence now we have, begin mathsize 12px style P subscript 1 over r cubed space minus space P subscript 0 over n equals fraction numerator 8 T over denominator r d end fraction end style.........................(2)
By eliminating P1 from (1) and (2) and after simplification, we get begin mathsize 12px style T space equals space fraction numerator open parentheses n minus r cubed close parentheses over denominator n open parentheses r squared minus 1 close parentheses end fraction cross times d over 8 cross times P subscript 0 end style
Answered by Expert 30th November 2018, 12:47 PM
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