[ELI5] Can someone explain Square Cube Law and how would applying it to HVAC/Heater units save electricity?

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Suppose a much larger house using less electricity using these methods?

In: Engineering

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Anonymous 0 Comments

The Square-Cube Law says that when you make an object larger by some amount, the surface area increases by the *square* of that amount, and the volume increases by the *cube* of that amount.

If you have a 1ft x 1ft x 1ft box, its surface area is 6 ft^(2) and its volume is 1 ft^(3). Now let’s make the cube twice as big, so now it’s 2 ft x 2 ft x 2 ft. The surface area is now 24 ft^(2), while the volume is now 8 ft^(3). When you made it 2x bigger, the surface area became 4x bigger (your 2x increase *squared* == 2^(2)x bigger == 4x bigger), while the volume became 8x bigger (your 2x increase *cubed* == 2^(3)x bigger == 8x bigger).

I can’t imagine how this could possibly be applied to making HVAC cheaper – it does the opposite, in fact. HVAC systems affect some volume of air, so a larger house has a massively larger volume of air and needs a stronger HVAC system which uses more electricity.

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