Computers are more energy efficient when they are kept at a lower temperature. But what is the reason? Also, do computers run fast when they are kept colder? Is this very significant as far as the average computer user is concerned?
Well, we cool modern processors not to make them more efficient, but so that the microchips do not get damaged by excessive heat. All electronic devices create waste heat based on the wattage of the device. Do you have a 65W CPU? Then you have to dissipate that heat safely using a heat sink (usually aluminum or copper with lots of fins and a fan to move heat from the chip into the air). Maybe a water cooling block (water is circulated through a metal block pressed on the processor, then through a radiator that transfers the heat to the air).
To ‘overclock’ a processor doesn’t make it more efficient but makes it faster. In fact, this often requires that you put more electricity into the chip than it was designed to carry. This causes even more heat to be generated and so even more exotic heat management systems must be used to keep the CPU cool (like a refrigeration system or simply pouring liquid nitrogen directly on the chip). Think of this as a drag racer vs a Prius. The drag racer will leave the Prius in the dust, but guzzles gallons of fuel, while the Prius sips ounces. The Prius is efficient. The drag racer is fast.
Increased resistance when wires heat up
Wires or traces on a circuit board do gain more resistance as they heat up. This means that they are slightly worse at transmitting electricity the hotter they are. But this doesn’t really come into effect very much at the temperature that computers operate. The cooling is there to prevent the outright destruction of the chip, not as a means for efficiency.
The last thing to note is that many computers have what’s called ‘thermal throttling’. If the system detects it’s chips are getting too hot, it will either slow them down (reducing the amount of electricity going through them and thus reducing heat) or completely shut down the system to prevent damage. This mostly affects laptops (which are thin and have thinner heat sinks and can get dust, hair, and junk in their cooling systems from being on your lap, couch or in coffee shops). This is the only cooling issue that would affect normal users. It’s either working as intended or slowed down. Unless you’re messing with overclocking, more cooling will not increase performance or efficiency in a noticeable way.
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