# Newton's Law of Cooling and Stefan's Law

• Noone1982
In summary, you are interested in studying the temperature change of objects using both Newton's law of cooling and Stefan's law. To simulate this, you can use the provided equations to calculate the rate of temperature change for each system, taking into account external factors like convection and radiation. Incorporating specific heat capacity and mass into the equations can provide a more accurate simulation.
Noone1982
I am trying to relate an object temperature as a function of time using Stefan's Law. Newton's law of cooling is,

$$\frac{dT}{dt}\; =\; k\left( T-R \right)$$

Where T is temp, t is time, k is a constant, and R is the temperature of the surroundings. Stefan's Law is,

$$P\; =\; e\sigma AT^{4}$$

where e is emmistivity, A is area, T is temperature and sigma a constant. I want to simulate two systems of differing temperature changing temperature by exchanging heat through some surface all the while emitting heat into the surroundings.

Hello, thank you for your post. It seems like you are interested in studying the temperature change of objects using both Newton's law of cooling and Stefan's law. These laws are important in understanding how objects exchange heat with their surroundings and how their temperature changes over time.

To simulate two systems of differing temperature changing temperature, you can use the equations you provided to calculate the rate of temperature change for each system. For example, if one system has a higher temperature (T1) and is losing heat to the surroundings at a rate of k(T1-R), while the other system has a lower temperature (T2) and is gaining heat from the surroundings at a rate of eσA(T2^4), you can set up a system of equations to solve for the temperatures over time.

One important thing to consider is that both Newton's law of cooling and Stefan's law assume that the objects are in a vacuum or in still air. If you are trying to simulate these systems in a real-world environment, you may need to also consider other factors such as convection and radiation from other sources.

Additionally, you may want to take into account the specific heat capacity of the objects, which will affect how quickly their temperatures change. You can incorporate this into your equations by using the specific heat capacity (c) and the mass (m) of the objects to calculate the change in temperature over time: dT/dt = (k(T-R) - eσA(T^4))/ (mc).

I hope this helps in your simulation and understanding of these important laws in thermodynamics. Good luck with your research!

## What is Newton's Law of Cooling?

Newton's Law of Cooling is a physical law that describes the rate at which an object cools down when it is in contact with a cooler surrounding environment. It states that the rate of cooling is proportional to the temperature difference between the object and its surroundings.

## What is Stefan's Law?

Stefan's Law, also known as the Stefan-Boltzmann Law, is a physical law that describes the relationship between the temperature and the amount of thermal radiation emitted by an object. It states that the total energy emitted per unit surface area of an object is proportional to the fourth power of its absolute temperature.

## How are Newton's Law of Cooling and Stefan's Law related?

Newton's Law of Cooling and Stefan's Law are related because they both describe the transfer of heat energy between an object and its surroundings. Newton's Law of Cooling focuses on the rate at which an object cools down, while Stefan's Law focuses on the total amount of thermal radiation emitted by an object. Both laws involve temperature differentials and constants of proportionality.

## What are some real-life applications of Newton's Law of Cooling and Stefan's Law?

Newton's Law of Cooling and Stefan's Law have many real-life applications. For example, they are used in the design of refrigeration and air conditioning systems, as well as in predicting the cooling rates of hot beverages and foods. These laws are also important in understanding the Earth's climate and the behavior of stars and other celestial objects.

## Are there any limitations or exceptions to Newton's Law of Cooling and Stefan's Law?

While Newton's Law of Cooling and Stefan's Law are generally accurate, there are some limitations and exceptions. For example, they assume that the object is in a perfectly insulated environment and that the cooling or heating is primarily due to radiative heat transfer. In addition, these laws may not apply to objects with extremely high or low temperatures or to objects that undergo phase changes.

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