I was curious to get a better sense of how much heat our servers will output.

\[\Delta T = \frac{Q}{mc}\]

Google tells me that the specific heat for air given a constant volume is 0.718kJ/kg K. Our room in Boelter Hall is about 50 cubic meters, so using the density of air at STP,1 that’s about 60 kg of air. Let’s just consider all 14 GPUs running at full-tilt: NVIDIA says that a 3090 has a TDP of 350W, giving us a total of 4.9kW, that is, about 5kJ per second, or 300kJ per minute.

Putting it all together:

\[\Delta T = \frac{300\rm{kJ}}{(60\rm{kg})(0.718\rm{kJ}/\rm{kg\ K})}\approx 7\rm{K}\]

Which is 12.5 degrees Fahrenheit per minute!

  1. Obviously this isn’t quite accurate, but it’s close enough. ↩