- #1

fishspawned

- 66

- 15

Lets say I have a situation where i am increasing an object's heat energy at some specific rate - for arguments sake, it's 2 degrees every second. If you like we can also rewrite this as an increase of energy of 2 Joules every second. Either will be fine.

let's make it super simple and call it:

**dQ/dt [warming] = 2**

I am wondering how to incorporate cooling. While this object is being warmed, it is also being cooled.

Newtons 's law of cooling is a function of time with a fixed beginning and ending temperature.

**dQ/dt [cooling] = h x A x (T(t) - Tenv)**

here h is the transfer coefficient, A is the transfer area, T is the temperature at a certain time, and Tenv is the ambient room temperature.

here h is the transfer coefficient, A is the transfer area, T is the temperature at a certain time, and Tenv is the ambient room temperature.

But what if you are simply starting from room temperature and raising it over time? The rate of cooling is changing as the temperature difference is changing due to the warming.

Is there an appropriate approach to this problem that would determine how much more time it would take for an object to warm to a certain temperature if we also included cooling into the picture? How can i combine the two equations in a sensible way?]

Any help would be greatly appreciated. Thanks