What is the purpose of a cooler? It's to keep the cold stuff cold, right?
A couple of months ago, my cousin's sports group were selling these insulated tumblers. The ad for the tumbler states that it will keep hot drinks hot for 6 hours, and cold drinks cold for 12 hours. I've seen these claims for other drink containers and I often puzzled why it would make a difference if the liquid is hot or cold? Wouldn't the heat transfer from the liquid to the air (or vice versa) be the same regardless if the container is resisting heat flow in or out of the container?
So I decided to do some analysis:
First I had to define a few things:
Hot drink = boiling water = 100C
Cold day (when you would want a hot drink) = 0C
Cold drink = 0C
Hot day (when you would want a cold drink) =30C
Room temperature ~= 23C
Definition of when a hot drink is no longer hot? 23C
Definition of when a cold drink is no longer cold? 23C
Then I made a spreadsheet using the heat transfer equation for the change in temperature of an insulated substance over time. I graphed this for both cases (Hot drink, cold day ; Cold drink, hot day)
Not surprisingly, the hot and cold drinks reached room temperature after the same time, about 5 hrs in my example.
So I thought a bit more and I added ice to the cold drink. Well when changing ice to liquid water it takes 80 calories per gram. While the ice is melting the temperature remains at 0C. So for a good amount of time, the drink remains cold while the ice is melting, once all the ice is melted, then the drink can warm up at 1C per gram per calorie added.
The graph shows this (green line) where the cold drink now reaches room temperature after 10 hours.
My conclusion is that there is no magic in the container. It will keep cold drinks cold for twice as long as keeping hot drinks hot, but only if there is a significant amount of ice.
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