A large number of water drops each of radius r combine to have a drop of radius R. If the surface tension is T and the mechanical equivalent of heat is J, then the rise in temperature will be

Question

Infinity Learn · Accepted Answer

Conserving volume,n×$$43$$$$π$$$$r3=43$$$$π$$$$R3$$⇒$$nr3=R3$$ Decrease in surface area $$=n$$×$$4$$$$π$$$$r2$$−$$4$$$$π$$$$R2$$⇒Δ$$A=4$$$$π$$$$R3(1r$$−$$1R)$$ Energy $$released=W=T$$× decrease in surface $$area=T$$×$$4$$$$π$$$$R3(1r$$−$$1R)$$ Heat produced, $$Q=WJ=4$$$$π$$$$TR3J(1r$$−$$1R)Also$$,$$Q=ms$$Δ$$T=43$$$$π$$$$R3$$×$$1$$×$$1$$×ΔT∴$$43$$$$π$$$$R3$$×$$1$$×$$1$$×Δ$$T=4$$$$π$$$$TR3$$ $$J(1r$$−$$1R)$$⇒Δ$$T=3$$ T $$J(1r$$−$$1R)$$

A large number of water drops each of radius r combine to have a drop of radius R. If the surface tension is T and the mechanical equivalent of heat is J, then the rise in temperature will be

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