A large number of identical small liquid drops, each of radius r , coalesce to form a single large drop of radius R . If the entire surface energy released during this process is converted into heat, the rise in temperature of the liquid is (Given: surface tension of the liquid is T , density of the liquid is , and its specific heat capacity is s )

Step-by-step solution

Let the total volume of the liquid be V . The volume of the large drop is V = 4 3 R^3 . The final surface area of the large drop is A_f = 4 R^2 = 3V R . If there are N small drops, the total volume is also V = N 4 3 r^3 . The initial total surface area of all small drops is A_i = N 4 r^2 = V 4 3 r^3 4 r^2 = 3V r . The decrease in surface area during coalescence is: A = A_i - A_f = 3V ( 1 r - 1 R ) The surface energy released is: E = T A = 3VT ( 1 r - 1 R ) This energy is converted into heat Q , which raises the tem