Calories, power dissipation, and environmental chambers

I was having a bottle of iced tea one day when I noticed something. Please see this excerpt from the bottle’s label referring to a 2,000 calories per day of personal intake (Figure 1).

I confirmed that caloric number independently to learn that it’s considered an average, but still an essentially correct daily caloric intake number.

Figure 1 Bottle label excerpt referring to a 2000 calories per day standard diet.

If we look up the word “calorie”, we find that one calorie equals 4.184 Joules (Figure 2).

Figure 2 A quick word search reveals that a single calory is the equivalent of 4.184 Joules.

If then we consume 2000 calories per day, we find the following in Figure 3.

Figure 3 The human body power usage based upon the 2,000 calories per day reference for a standard diet.

Two thousand calories per day equals 8368 joules per day which then comes to 0.096852 joules per second which is just under 97 mW. We’ll call that 100 mW just for convenience of thought. We are dealing with approximations, of course.

If all of one’s caloric intake is ultimately dispersed as body heat, that 100 mW of body heat could plausibly be imparted to whatever delicate unit under test (UUT) one happens to be working on while working diligently inside an environmental test chamber.

I once saw such an environmental test chamber in which there was a bank of 100-W lamps mounted “over there”. Those lamps were kept constantly lit and running except that if one more person were to enter the room, one lamp would then be extinguished. This was supposed to help hold the thermal environment of the UUT as invariant as possible.

If we say the following:

That each light bulb was providing 100 W over a spherical area of 4*π*R² where R is the radial distance from the light bulb
That the UUT has 1 square foot (1 ft2)of presented area receiving that bulb’s thermal radiation
That the bulk of the 100 mW of a human body was also impinging on that UUT

We can then seek that value of R for which the 100 W  of one bulb was down by a factor of 1000 to yield the equivalent human presentation of 100 mW to that UUT.

Noting that 100 W divided by 100 mW equals 1,000, we seek that value of R at which the area of the posited sphere around the bulb comes to 1,000 ft2.

Where 4*π*R² = 1,000, we find that R is nominally 8.92 ft.

For all of these crude approximations, y’know what?? That is indeed just about how far away those light bulbs were positioned with respect to the UUT at hand in that chamber.

John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).

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