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While water is being heated, vapour bubbles form at the bottom of the vessel, then detach and rise. Model each bubble as a sphere of radius R that makes a circular line of contact of radius r with the bottom of the vessel. Given r << R and that the surface tension of water is T, the radius R just before a bubble detaches is given by (density of water = rho_w):
- R² * sqrt(rho_w*g / T)
- R² * sqrt(3*rho_w*g / T)
- R² * sqrt(rho_w*g / (3*T))
- R² * sqrt(rho_w*g / (6*T))
Correct answer: R² * sqrt(rho_w*g / (3*T))
Solution
The original question asks for the contact radius r in terms of R (the printed stem is truncated). At the verge of detachment, buoyant force equals the vertical surface-tension pull around the contact ring. Equating and using r << R yields r = R²*sqrt(rho_w*g/(3T)).
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