Question

Two spherical bubbles coalesce. V is the consequent change in volume and S is the total change in surface area then

• A. 3 PV + 4ST = 0
• B. 4PV + 3ST = 0
• C. 2PV + 3ST = 0
• D. 3PV + 2ST = 0

Answer 1

Answer: (A)

3 PV + 4ST = 0

Answer 2

P₁V₁ + P₂V₂ = P₃V₃

or $\left( \mathrm { P } _ { 0 } + \frac { 4 \mathrm {~T} } { \mathrm { r } _ { 1 } } \right) \left( \frac { 4 } { 3 } \pi \mathrm { r } _ { 1 } ^ { 3 } \right) + \left( \mathrm { P } _ { 0 } + \frac { 4 \mathrm {~T} } { \mathrm { r } _ { 2 } } \right) \left( \frac { 4 } { 3 } \pi \mathrm { r } _ { 2 } ^ { 3 } \right)$

=

or 4T(r₁² + r₂² - r) = - P₀(r₁³ + r₂³ – r³)

4T

or 4TS + 3P₀V = 0