# Inverse Square Law, Temperature Change, and Heat Source Temp

• I
I've been trying to wrap my head around the relationship between temperature increase of an object at a distance and temperature of a heat source. From what I've found, the temperature increase of an object from thermal radiation is affected by the inverse square law. This classroom experiment seems to show an inverse-square relationship between temperature change and increasing distance, and I've found similar answers elsewhere.

Is it possible to determine the temperature of a heat source based on temperature increase of an object a certain distance away? Would this work for much larger scales? For example, if an object (say, in a vacuum to keep things simple) is 500 radii away from the heat source and experiences a temperature increase from 298 K to 300 K, does that mean the temperature of the heat source is (300 K * 500^2) = 75,000,000 K?

Simon Bridge
Homework Helper
Welcome to PF;
The rate of thermal radiation depends on the 4th power of it's temperature (for a blackbody).
The flux falls off by the inverse square law because of geometry.
The rate of temperature increase depends on how much of the flux is absorbed by the target and it's specific heat.
A blackbody target will absorb the lot, otherwise you need the energy absorbtion profile.
But, in principle, the temperature increase of a local object is related to the temperature of a distant object - it is difficult, in general, to account for the effect of all possible alternative heat sources on local temperature. It is usual to determine the temperature of a distant object from it's spectrum.

I had no idea there was a Sci-Fi and Fantasy sub-forum here. I was involved in a discussion about a fictional weapon heating the atmosphere to create a warm front and wanted to quantify how hot a heat source would have to be to heat the atmosphere 4,000 radii away by 10 K. I know this wouldn't make any sense in real life, but I was wondering if this method could work to get a reasonable estimate or a minimum for the hypothetical temperature. Should I move to that sub-forum, or is it not accurate gauge heat source temperature this way?