It's a hot summer day and you've just had some refreshing salad. Unfortunately all the veggies seem to have caused some... gas. Is this good news, or bad news, as far as the physical temperature of the room?
We can treat the fart as a quantity of slightly compressed gas trapped in a rigid, warm vessel. When the gas escapes, its partial pressure will drop while volume increases and therefore it seems like the temperature should slightly drop. On the other hand, the total pressure of the room should slightly increase (if we assume little air flow in/out - bad idea I know). Moreover, as the gas mixes with the room air, perhaps that would result in a more efficient transmission of heat from gas to room air, as opposed to from gas to rigid vessel to room air?
Trying to reason holistically rather than from first principles, it seems like a compressed quantity of gas in a vessel has lower entropy than a dispersed gas. This increase in entropy seems like it would be accompanied by a proportional increase of heat.
Which process prevails? Does the cooling from expansion overpower the warming up from increased pressure and more efficient dispersion? Is the net effect on the room's temperature large, or is it comparatively negligible due to these opposing effects?
For the sake of precision, we can take:
- Room temperature as 32C
- Vessel as 37C in thermal equilibrium with the escaping gas
- Room is a cube 4x5x2 m large
- The room is almost airtight but not quite, there is a small gap under the door such that air flux is very small but nonzero
- The air inside the room is efficiently circulated with a fan