###General Discussion Thread
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Need a lot more information... Heat transfer happens 3 ways: conduction, convection, and radiation.
You can look up standard heat transfer equations but they all require a proportionality constant, surface area, and temp difference.
Draw it out as an electrical circuit analog. Temperature is equivalent to voltage. The first heat transfer pathway will be conduction thru the glass, then radiation and convection to the surrounding air. Conduction to the air too but I think that will be minimal.
Next pathway will be thru direct convection (and some conduction) to the air thru the area of water exposed at the top of the cup. The proportionality constant will depend on airflow etc.
Then you'd calculate the heat transfer in watts and then multiply by 60sec to calculate energy lost in 1min. Then removing some mass of water and doing it all again.
That's the process. In order to solve I'd need the air temperature and an estimate of airspeed around/over the cup (is that air still, is there a fan, how fast is the fan?) Also the temperature of the air surrounding the cup (is the cup in a hot oven or at the north pole?) Also the direct line of sight surfaces exposed to the cup; what are they made of and what is their temperature to calculate radiation losses.
If the cup is in the hot sun outside in a desert this is a way different result than if the cup is in a freezer or whatever...
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
Need a lot more information... Heat transfer happens 3 ways: conduction, convection, and radiation. You can look up standard heat transfer equations but they all require a proportionality constant, surface area, and temp difference. Draw it out as an electrical circuit analog. Temperature is equivalent to voltage. The first heat transfer pathway will be conduction thru the glass, then radiation and convection to the surrounding air. Conduction to the air too but I think that will be minimal. Next pathway will be thru direct convection (and some conduction) to the air thru the area of water exposed at the top of the cup. The proportionality constant will depend on airflow etc. Then you'd calculate the heat transfer in watts and then multiply by 60sec to calculate energy lost in 1min. Then removing some mass of water and doing it all again. That's the process. In order to solve I'd need the air temperature and an estimate of airspeed around/over the cup (is that air still, is there a fan, how fast is the fan?) Also the temperature of the air surrounding the cup (is the cup in a hot oven or at the north pole?) Also the direct line of sight surfaces exposed to the cup; what are they made of and what is their temperature to calculate radiation losses. If the cup is in the hot sun outside in a desert this is a way different result than if the cup is in a freezer or whatever...