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Paula Fino
Carlos Parrado
03/04/2020
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.
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.
"The temperature of a body changes at a rate that is proportional to the difference in temperatures between the external environment and the body"
Where:
T = body temperature
t = time
Tm = ambient temperature
Equation (1) can be solved using the separable variables method:
Integrating on both sides (2):
Is obtained:
It is simplified (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.
1. What is the body temperature after 5 min?
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.