Question
State and prove Newton’s law of cooling.
Solution
Newton's law of cooling states that the rate of fall of temperature of a hot body is directly proportional to the temperature difference between the body and surrounding when temperature difference is small.
Proof:
Let a body of mass m, surface area A and emissivity e be heated to a temperature T and placed in an enclosure maintained at temperature T0.
The rate of loss of heat by radiation from body is,
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If dT is the change in temperature of the body due to loss of heat, then
where,
s is the specific heat of the body.
From equation (1) and (2), we have
Proof:
Let a body of mass m, surface area A and emissivity e be heated to a temperature T and placed in an enclosure maintained at temperature T0.
The rate of loss of heat by radiation from body is,
If dT is the change in temperature of the body due to loss of heat, then
where,
s is the specific heat of the body.
From equation (1) and (2), we have
