Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer
A metal ball of mass 1 kg is placed in a room at 20^ C and heated using a 20 W heater. The steady-state temperature of the ball is observed to be 50^ C . Assuming the ball's temperature rises uniformly from 20^ C to 30^ C in 5 minutes, calculate the specific heat capacity of the metal.
Options
- A400 J kg ⁻¹ K ⁻¹
- B1000 J kg ⁻¹ K ⁻¹
- C500 J kg ⁻¹ K ⁻¹
- D600 J kg ⁻¹ K ⁻¹
Correct answer
C. 500 J kg ⁻¹ K ⁻¹
Step-by-step solution
Rate of heat loss to the surroundings is given by Newton's law of cooling: dQ_ loss dt = K(T - T₀) At steady state, the temperature is constant at T_s = 50^ C , so the heat supplied by the heater equals the heat lost to the surroundings: P = K(T_s - T₀) 20 = K(50 - 20) K = 20 30 = 2 3 W ^ C ⁻¹ During the heating from 20^ C to 30^ C , the average temperature of the ball is: T_ avg = 20 + 30 2 = 25^ C Since the temperature rises uniformly, the average rate of heat loss is evaluated at the average temperature: P_ loss