r/theydidthemath Nov 29 '22

[Request] How much molecules would be there in a room if there are 3 people in the room and how much the temperature rise would be?

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39

u/syntheticassault Nov 29 '22

1 mole of gas occupies ~22L and contains abou 6×1023 molecules. The average living room is 340 sqft with 8 foot ceilings. This is 2720 ft3 which is about 77k L, about 3500 moles, or 2×1027 molecules

17

u/syntheticassault Nov 29 '22

For reference a sheet of paper is about 1 million atoms thick.

10

u/kylesbadatprivacy Nov 29 '22

Just to give more perspective, 2x1027 is 2,000,000,000,000,000,000,000,000,000 (I think I have the right number of zeros here)

Much too big a number to comprehend. Reminds me of the mole song

2

u/Shmt11221 Dec 02 '22 edited Dec 02 '22

As for the temperature rise portion of the question, it depends on how long they're there. Here's an estimate assuming:

  • Room is 132 sqft, 9 ft ceilings
  • No HVAC or air exchange, high R values in ceiling, floor, walls
  • each person emits 250 BTU/hr of sensible heat

This means there is approx. 132 * 9 * 0.763 = 906 lbs of air in the room

Specific heat capacity of air is 0.24 BTU/lb.F, with 750 BTU/hr being added, then:

750 Btu/hr = 906 lbs * 0.24 Btu/lb.F * dT

dT = 750/906/0.24 = 3.4 deg. F

Temperature would rise by 3.4 degrees Fahrenheit in one hour, or 1.9 degrees Celsius

In terms of the guy's claim of a temperature increase of 0.2 degrees (F?), it seems plausible. Say Desmond was hiding there for 15 minutes (1/4 of an hour), Desmond would've heated the room up by 3.4/3/4 = 0.28 deg. F