If say the temperature of just one component of air e.g. water vapor suddenly rises (say through IR absorption), what method can be used to very roughly and quickly calculate the amount of time it will take for the temperature to even out?
Heat conduction is... well governed by the heat conduction equation which is a first order equation with respect to time and second order with respect to spatial dimensions. It would be hard to estimate the system with an easier equation without seeing what the system configuration is.
I believe the problem, as posed, suggests that one component, intimately mixed with the other components becomes hotter than that other components, so one would need to derive an effective conductivity between the hot molecules and the colder molecules.
A similar issue is found in fusion plasma physics where electrons can be heated then they transfer thermal energy to the ions, or hotter ions are injected into a colder plasma - but this latter example involves a spatial dependence - unlike the OP.
Hmm, I've never thought about a problem regarding mixes fluids of different temperature together and timing their approach to equilibrium. I'm blank on what model to use. You'd have alot of convection, and conduction all happening at once together in the mixture... although I've never heard of it, the effective conduction may be the way to go for an estimate.
We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling We Value Civility
• Positive and compassionate attitudes
• Patience while debating We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving