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, and further assuming th
Options
- A5.55 s
- B5.88 s
- C5.00 s
- D5.26 s
Correct answer
D. 5.26 s
Step-by-step solution
Let P be the power of the heater and k be the cooling constant. Just after the heater is turned on at 20^ C , the temperature difference with the surroundings is zero, so the heat loss is zero. The rate of heat supplied is entirely used to increase the temperature: P = C ( dT dt )_ initial = 80 2 = 160 W Just after the heater is turned off at 30^ C , the rate of heat loss is: P_ loss = C (- dT dt )_ cooling = 80 0.2 = 16 W According to Newton's law of cooling, the rate of heat loss is proportional to the temperatur