Newton studied the cooling rate of the same object, and found that the cooling rate of the same object is related to the temperature difference between the outside and the object under the condition that the nature and temperature of the external medium are the same and the nature and surface area of the same object are the same.

The temperature of a hot object is t, ignoring the changes of surface area, external medium properties and temperature. Its cooling rate (dt/dt) is different from other objects.

The difference (t-c) between the temperature of the object and the temperature of the surrounding environment is directly proportional, that is, dt/dt=-k(t-c), where t is time and k is constant.

The calculation method is:

correct

Dt/dt=-k (temperature coefficient)

Through integration, you will get

Ln(t-c)=-kt+b(b is an integer constant)

(t-c)=e^(-kt+b)

( 1)

Let t=0, that is, the initial temperature of the object, (1) becomes

(t0-c)=e^b

Then replace

( 1)

get

t=c+(t0-c)^(-kt)

Calculate b and k, substitute the value of t, and calculate the temperature of the object at a certain moment.

It is deduced from the cooling law that the temperature of an object changes more and more slowly when the surface area, the nature of the external medium and the temperature are ignored.