Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer
Inside a room at 20^ C , a metal ball of mass 1 kg is heated by a 20 W heater. The temperature of the ball reaches a steady state at 50^ C . Assuming Newton's law of cooling holds true, calculate the rate of loss of heat to the surrounding when the ball's temperature is 30^ C .
Options
- A10 W
- B10 3 W
- C15 W
- D20 3 W
Correct answer
D. 20 3 W
Step-by-step solution
At steady state, the rate of heat supplied by the heater is equal to the rate of heat lost to the surroundings. According to Newton's law of cooling, the rate of heat loss is proportional to the temperature difference between the body and the surroundings: dQ dt = K(T - T₀) Given that the heater supplies 20 W and the steady-state temperature is 50^ C in a room at 20^ C : 20 = K(50 - 20) 20 = 30K K = 2 3 W/ ^ C When the temperature of the ball is 30^ C , the rate of heat loss to the surroundings is: dQ' dt = K(30 -