Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer
A metal block having a heat capacity of 80 J ^ C ⁻¹ is located in a room at 20^ C and is heated electrically. Once the temperature attains 30^ C , the heater is turned off. Just after the heater is turned on, the block's temperature increases at a rate of 2^ C s ⁻¹ , and just after it is turned off, the temperature decreases at a rate of 0.2^ C s ⁻¹ . Assuming Newton's law of cooling is valid, determine the power of
Options
- A160 W
- B40 W
- C320 W
- D80 W
Correct answer
A. 160 W
Step-by-step solution
Let the power of the heater be P and the cooling constant be k . According to Newton's law of cooling, the rate of change of temperature of the block when the heater is on is given by: C dT dt = P - k(T - T₀) where C = 80 J ^ C ⁻¹ is the heat capacity and T₀ = 20^ C is the room temperature. Just after the heater is turned on, the temperature of the block is equal to the room temperature, T = 20^ C . Since T = T₀ , the rate of heat loss to the surroundings is zero. Substituting the given rate of heating dT dt = 2^ C