Question

Compare the rate of loss of heat from a metal sphere at 827°C with the rate of loss of heat from the same at 427°C, if the temperature of surrounding is 27°C.

Hint:

The rate of heat loss is directly proportional to the temperature difference between the object and its surroundings.

Answer 1

Step 1: Newton's Law of Cooling.
According to Newton's law of cooling, the rate of heat loss \( \frac{dQ}{dt} \) is given by: \[ \frac{dQ}{dt} = k \cdot (T
- T_s) \] where \( k \) is the heat transfer constant, \( T \) is the temperature of the object, and \( T_s \) is the surrounding temperature.
Step 2: Calculate Rate of Heat Loss.
For the metal sphere at 827°C: \[ \frac{dQ_1}{dt} = k \cdot (827
- 27) = k \cdot 800 \] For the metal sphere at 427°C: \[ \frac{dQ_2}{dt} = k \cdot (427
- 27) = k \cdot 400 \] Thus, the rate of heat loss is twice as much at 827°C compared to 427°C.