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JEE Main 2014 · 12 Apr · Shift 1, Physics question 10

Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S the change in total surface area, T is the surface tension and P atmospheric pressure, which of the following relation is correct ?

Choose one option
Answer and worked solution

Official answer: B

Inside a soap bubble p=P+4Trp=P+\frac{4T}r. Air is conserved and (isothermal) ∑pV\sum pV is constant:
P∑V+4T3∑4πr2 is constant.P\sum V+\frac{4T}3\sum4\pi r^2\text{ is constant}.
So P ΔV+43T ΔS=0P\,\Delta V+\frac43T\,\Delta S=0, i.e. 3PV+4ST=03PV+4ST=0.

Topics:Surface tensionIdeal gas equation
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