Answer to Question #164931 in Physics for Simon

Question

A bath contains 50Kg of water at 75%. Hot and cold taps at temperatures of 85° and 25° respectively are turned to deliver 10 Kg of water per minute. How long will it take for the temperature of bath to drop to 60° ? (Specific heat capacity of water is 4,200 J/Kg-1/K-1)

Answer 1

$$Mc(T_1-T)+\frac{dm}{dt}c(T_2-T)t=\frac{dm}{dt}c(T-T_3)t\\ 50(75-60)+10(85-60)t=10(60-25)t\\t=7.5\ min$$