# Thermal time constant versus specific heat

#### Article By : John Dunn If we know the specific heat capacity of a particular thing, we can make an estimate of the time constant of that particular thing undergoing a thermal excursion.

Quite some years ago I examined how, if we know the specific heat capacity of a particular thing, we can make an estimate of the time constant of that particular thing undergoing a thermal excursion (see Thermal Time Constant and Specific Heat). However, some additional commentary is warranted. Figure 1 This diagram shows the thermal resistance and thermal capacitance of a heat sink mounted to a heat dissipating surface.

Imagine that you have some particular object such as a heat sink consisting of some particular material and mass which is attached to some heat source such as power dissipating electronic components.

Let us also make the simplifying assumption that there is zero thermal resistance between the volume portions of the heat sink itself so that the temperatures of all the little bits of the total mass are the same throughout—in other words, there is zero thermal gradient throughout the heat sink.

The mass thus described will behave as a thermal capacitance. Now, hold that thought.

That mass will also be interfaced to some kind of mounting surface and the interface between the two will have some value of thermal resistance. Hold that thought too.

The usual heat sink material of choice would be aluminum. That metal has a specific heat of 0.9 joules per degree Celsius per gram or 0.9 joules / °C / gram. If we take the mass in grams and multiply that by the specific heat, we get a value for the thermal capacitance.

Assuming a thermal resistance of 0.1°C per watt and an aluminum mass of one kilogram, we would see the following numerical result: Figure 2 This table shows the numerical result of a thermal time constant calculation assuming a thermal resistance of 0.1°C per watt and an aluminum mass of one kilogram.

If we doubled the thermal resistance, we’d get double the thermal time constant: Figure 3 If thermal resistance is instead 0.2°C per watt—double that of the previous calculation—the thermal time constant is also doubled.

The issue here that was not addressed in the prior essay is that if you are measuring the temperature rise of some heat sink and you cavalierly say “Oh it’s been a minute or so and things look okay,” you may end up overlooking a crucial temperature rise by having halted your observations too soon.

Please don’t overlook your thermal time constant(s). They can be surprisingly long. 