A vessel filled with air under pressue `p_(0)` contains a soap bubble of diameter `d`. The air presuue have been reduced `n`-fold, and the bubbled diameter increased `r`-fold is othermally. Find the surface tension of the soap water solution.
Text Solution
Verified by Experts
For the air enclosed in the bubble we have `pV=nRT` `implies(p_(0)(8T)/d)pi/6d^(3)=(p_(0)/n+(8T)/(rd))pi/6r^(3)d^(3)` `impliesp_(0)+(8T)/d=(p_(0)r^(3))/n+(8Tr^(2))/d` `impliesp_(0()1-r3/n)=(8T)/d(r^(3)-1)impliesT=1/8p_(0)d xx(1-(r^(3))/n)/(r^(2)-1)` `impliesp_(0)(1-(r^(3))/n)=(8T)/d(r^(2)-1)impliesT=1/8p_(0)d xx(1-(r^(3))/n)/(r^(2)-1)`
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CENGAGE PHYSICS-PROPERTIES OF SOLIDS AND FLUIDS-INTEGER_TYPE
