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Applications in population dynamics and cooling law

Paula Fino

Carlos Parrado

03/04/2020

Newton's law of cooling

Newton's law of cooling

When the temperature difference between a body and its environment is not too great, the heat transferred in the unit of time to the body or from the body by conduction, convection, and radiation is approximately proportional to the temperature difference between the body and the external environment.

Cooling Law Applications

Newtonian cooling is currently used especially in climate models as a fast and less computationally expensive way of calculating the temperature evolution of the atmosphere. These calculations are very useful for determining temperatures as well as for predicting the events of natural phenomena.

1

"The temperature of a body changes at a rate that is proportional to the difference in temperatures between the external environment and the body"

k>0

2

Where:

T = body temperature

t = time

Tm = ambient temperature

Equation (1) can be solved using the separable variables method:

Integrating on both sides (2):

3

Is obtained:

It is simplified (4) :

4

A body that has a temperature of 70 ° F is deposited (at time t = 0) in a place where the temperature is maintained at 40 ° F. After 3 min, the body temperature has decreased to 60 ° F.

5

1. What is the body temperature after 5 min?

6

2. How long will it take for my body to reach 50 ° F?

La rapidez o razón de cambio de la población (P) de una cierta comunidad es proporcional al tiempo.

Population growth problems

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  • http://www.sc.ehu.es/sbweb/fisica/estadistica/otros/enfriamiento/enfriamiento.htm

REFERENCES

  • https://sites.google.com/site/ecuacionesdiferentes/home/ley-de-enfriamiento-de-newton
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