Newton's Law of Cooling and Stefan's Law

[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.

 

[Jhero]

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!