Calculating resistor's temperature at equilibrium

I'm trying to characterise a resistor's temperature at equilibrium when I know the voltage on it and the ambient temperature. I have a few ways to measure but I get mixed results, so I'm searching for a theory to compare to. I'm a second year physics and EE student and I haven't done thermodynamics yet, so I'm kind of lost.

I can use curve fitting to find hard-to-reach constants like its heat capacity. I can also control the ambient temperature and the power supplied to it. In the measurements it seems like the temperature is rising exponentially (with a negative time factor).

Is there an equation or some models I can dive to?

Thanks in advance.

• The temperature of the resistor gets to is highly dependent on the environment around it and all the different ways that heat energy is flying out of it, conduction through leads, convection into the air. it's not a trivial problem. Commented Nov 28, 2019 at 19:40
• Resistors are always rated by power dissipation. It is one of the key components to a resistor spec sheets really resistor selection in general right behind the actual resistivity of it. That is really all you need to know unless you're using a resistor in a very non-conventional manner. Commented Nov 28, 2019 at 19:49
• One thing to know as an EE: Mechanical calculations of phenomena distributed over an area is never easy. An equation or model is usually nowhere near enough to actually tackle the problem. That's why those MechEs take so much math. As EEs, we're pretty lucky we can do quite a bit with lumped circuit models. MechEs aren't so fortunate. Commented Nov 28, 2019 at 19:51
• You have some really good comments, already, from MadHatter. With respect to DKNguyen's comments added to MadHatters, I also agree overall. Knowing the theory and, more important, knowing how to apply which theory where and how to combine the primary ones without getting bogged down in 3rd effects, takes experience and training. You might think it is as simple as just knowing the power, the thermal resistance to air, and the ambient temperature. But it's not. Resistors have leads, direct contacts, grime accumulation, and air circulates (or doesn't circulate) at differing rates, etc.
– jonk
Commented Nov 28, 2019 at 21:03
• @ChenTasker Then make measurements for your specific setups that none of us know anything about, decide on the theoretical model you need to parameterize, and then work out its parameters from the data you develop in testing. If your theoretical model is good enough, you may get the needed parameters with a minimal number of calibration runs.
– jonk
Commented Nov 29, 2019 at 3:27