Physical Significance

Note: My understanding is that the question is regarding the term "physical significance", not specifically Biot's number's physical significance. Therefore my question will focus on that and will merely indicate how to obtain Biot's number's significance. Actually doing so is left as an exercise to the reader.

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A property's "physical significance" means exactly what it seems to mean: what the property describes in the physical world. Basically, "physical significance" is a fancy term for "definition". Another way of looking at it is imagining you have an object or system and you want to measure some property; what exact physical characteristics do you need to measure to calculate this property?

For instance, what is the physical significance of temperature? Well, temperature is a description of how quickly the molecules of a given object are moving. That is temperature's physical significance. So, if you want to measure temperature, how would you do so? "Use a thermometer" isn't the answer I'm looking for, because it is merely an instrument, and I'm looking for the physical properties it measures. So, if you want to measure temperature, you could freeze the object in time and measure the speed of each of its particles (ignoring quantum uncertainty and the fact that "speed" makes no sense if you freeze time).

Biot's number is a representation of the temperature gradient to be expected within an object: if Biot's number is large, then the object's thermal conductivity is much smaller than its thermal film coefficient (times a volume/area coefficient).

But, again, what physical properties would you need to measure to calculate Biot's number? Thermal conductivity and film coefficients aren't (in my opinion) a satisfactory answer because they are derived properties, much as temperature is. So, keep it going. What physical properties would you need to measure to calculate thermal conductivity, for instance? Once you reach the fundamental physical properties of the object which define Biot's number, you can then define what relationship Biot's number actually describes, at which point you'll have obtained its physical significance.