A 20 W heater is used to heat a metal ball of mass 1 kg in a room at 20^ C . The ball eventually attains a steady temperature of 50^ C . Assuming the temperature of the ball increases uniformly from 20^ C to 30^ C over a period of 5 minutes, determine the total loss of heat to the surrounding during this time interval.

Step-by-step solution

At steady state, the rate of heat loss to the surroundings equals the power supplied by the heater. P = k(T_ steady - T₀) 20 = k(50 - 20) k = 20 30 = 2 3 W/ ^ C During the 5 -minute interval, the temperature of the ball increases uniformly from 20^ C to 30^ C . Since the temperature change is uniform, the average temperature of the ball during this time is: T_ avg = 20 + 30 2 = 25^ C The average rate of heat loss to the surroundings during this interval is: P_ loss = k(T_ avg - T₀) = 2 3 (25 - 20) = 10 3 W The tota