Question

Two soap bubbles combine to from a single bubble. In this process, the change in volume and surface are respectively V and A. If P is the atmospheric pressure, and T is the surface tension of the soap solution, the following relation is true

• A. $4PV+3TA=0$
• B. $3PV-4TA=0$
• C. $3PV+4TS=0$
• D. $5PV+6TS=0$

Answer 1

The correct option is C $3PV+4TS=0$

Change in pressure of bubble in air

$△P=\left(\frac{2T}{R}\right)\times 2=\frac{4T}{R}$

T= Temperature

R= Radius

$(P+\frac{4T}{r_1})\left(\frac{4\pi }{3}{r}_1^3\right)+(P+\frac{4T}{r_2})\frac{4\pi }{3}{r}_2^3=(P+\frac{4T}{r})\frac{4\pi }{3}{r}^3$

$PV+\frac{4T}{3}[4\pi r_1^2+4\pi r_2^{27}-4\pi r^2]20$

$3PV+4TS=0$