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Coffee Drinker

 
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GaryProtein



Joined: 26 Oct 2005
Posts: 535

PostPosted: Wed Jan 02, 2008 2:27 pm    Post subject: Coffee Drinker Reply with quote

My secretary plans on drinking her 12 ounce cup of coffee when she returns to her desk after filing some papers which will take about 10 minutes. She likes her coffee with some liquid non-dairy coffee creamer which is in half ounce sealed containers that are at room temperature. She likes her coffee as hot as possible and wants to know if she should add the creamer to the coffee as soon as she pours the coffee from the pot or just before she drinks it. Does it matter when she adds the creamer?

What should she do? As always, defend your answer. Smile
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Michael Chu



Joined: 10 May 2005
Posts: 1619
Location: Austin, TX (USA)

PostPosted: Thu Jan 03, 2008 8:08 pm    Post subject: Reply with quote

My guess would be to add the cream first... my reasoning in white:

Heat exchange rate is proportionate to the difference in temperature (from the coffee to the environment). If the coffee temperature is higher, then it will lose heat faster. So the coffee starts off losing a lot of heat and then less and less until the ten minutes is up.

If you pour a colder liquid into the coffee, then the heat loss to warm up the new liquid should be the same no matter when you pour it in. If you pour it in at the beginning, then the coffee temperature drops initially and then heat is exchanged with the environment slower than usual since a) you have more liquid at a given temperature and need more heat exchanged to drop the temperature and b) the average lower temperature means lower heat exchange.

If you pour in at the end, then the "rapid" heat exchange in our control case has already occurred and now, a great deal of heat will be lost to warming up the introduced liquid. Since the amount of heat lost is the same (beginning or end) the difference should be in the heat loss in between. The beginning mix one loses heat less rapidly, so it should be warmer.
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Auspicious



Joined: 29 Dec 2005
Posts: 58
Location: on the boat, Annapolis, MD

PostPosted: Mon Jan 07, 2008 9:17 pm    Post subject: Reply with quote

Michael is correct.

This is a classic mid-term exam problem in Thermodynamics.
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LoraineSmith56



Joined: 10 Dec 2011
Posts: 1
Location: Houston

PostPosted: Sat Dec 10, 2011 6:13 am    Post subject: Reply with quote

Very well explained by Michael thermodynamically.lol.
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