Understanding Newton's Law of Cooling: Definition, Equation, and Application

Newton's Law of Cooling and suggests switching the positions of T(t) and Ta in the equation. The speaker agrees and states that it makes sense for heat loss to be negative and heat gain to be positive. In summary, Chetan and the speaker discuss the convention and placement of variables in Newton's Law of Cooling.
  • #1
Arcthor
34
1
If the temperature of an object with temperature T(t) is place in a room with the ambient temperature Ta, Newtons Law of Cooling is defined as dT / dt = k (T(t) - Ta), correct?

This implies we would need a negative k-value. Wouldn't the equation therefore be described better if T(t) and Ta changed place? As in: dT / dt = k (Ta - T(t))

What am I missing?
 
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  • #2
The convention is somewhat arbitrary, but I think it makes sense for heat loss to be negative and heat gain to be positive.
 
  • #3
The firm of the equation I am familiar with is the one that you suggested.

Chet
 

1. What is Newton's Law of Cooling?

Newton's Law of Cooling is a physical law that describes the cooling of an object in a surrounding medium. It states that the rate of cooling of an object is directly proportional to the temperature difference between the object and its surroundings.

2. What is the equation for Newton's Law of Cooling?

The equation for Newton's Law of Cooling is: T(t) = T_s + (T_0 - T_s)e^(-kt), where T(t) is the temperature of the object at time t, T_s is the temperature of the surrounding medium, T_0 is the initial temperature of the object, and k is a constant.

3. How is Newton's Law of Cooling applied in real life?

Newton's Law of Cooling has various applications in everyday life, such as predicting the cooling of hot beverages, determining the time of death in forensic science, and understanding the cooling of electronics.

4. What are the assumptions made in Newton's Law of Cooling?

The assumptions made in Newton's Law of Cooling include: the object is in a closed system, the surrounding medium is well-mixed, and there is a constant temperature difference between the object and its surroundings.

5. How does Newton's Law of Cooling relate to the second law of thermodynamics?

Newtons's Law of Cooling is a direct application of the second law of thermodynamics, which states that heat always flows from a higher temperature to a lower temperature. This law explains the direction of heat transfer in Newton's Law of Cooling, where heat flows from the object to its surroundings until thermal equilibrium is reached.

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