Answer:
The rate of heat loss from the metal sphere at 827°C is twice the rate of heat loss from the same sphere at 427°C.
Explanation:
The rate of heat loss from an object can be determined using Newton's law of cooling, which states that the rate of heat loss is proportional to the temperature difference between the object and its surroundings. Mathematically, this is expressed as...
[tex]Q = k \Delta T[/tex]
Where...
- "Q" is the heat loss/gain
- "k" is the constant of proportionality which is the cooling constant
- "ΔT" is the change in temperature
[tex]\hrulefill[/tex]
For the sphere at 827°C:
[tex]\Delta T_1= 827\°C - 27\°C \\\\\Longrightarrow \boxed{\Delta T_1=800\°C}[/tex]
For the sphere at 427°C:
[tex]\Delta T_2= 427\°C - 27\°C \\\\\Longrightarrow \boxed{\Delta T_2=400\°C}[/tex]
Assuming that the cooling constant k remains constant, we can compare the rates of heat loss.
[tex]\dfrac{Q_1}{Q_2} =\dfrac{\Delta T_1}{\Delta T_2}\\\\\Longrightarrow \dfrac{Q_1}{Q_2} =\dfrac{800\textdegree C}{400\textdegree C} =\boxed{2}[/tex]
Thus, the rate of heat loss from the metal sphere at 827°C is twice the rate of heat loss from the same sphere at 427°C when the temperature of the surroundings is 27°C.
