# Insulated coffee cup mystery...

#### cmartinez

Joined Jan 17, 2007
6,789
Being an avid coffee drinker, I finally gave in to temptation and bought myself a stainless steel insulated cup (not of Yeti brand, which sell for a ridiculously high price), and I'm extremely happy with it...

Anyway, it's become obvious (and I've also checked online) that these things can keep liquids cold for a very long time. Leftover ice will linger in there for a little more than 24 hours if the lid is in place and properly shut. (Do they really hold a vacuum between their inner and outer walls, as this Amazon ad states?). But warm liquids are a different story, they will cool down to room temperature in about 6 hours.

My question is, why is this thing better at keeping something cold inside, than keeping it hot? Why is easier for heat to leak out instead of creeping in? I suspect it has something to do with the lid, since heat travels upward... but I'm not 100% sure.

#### jamiepatterson

Joined Apr 10, 2018
4
There are two things going on. First, the delta T for hot liquids is higher so you have a larger driving force. Coffee is brewed at 190 degrees F, room temperature is 68 degrees F, where as an iced drink is at 32 degrees F so the delta T is smaller for cold liquids. Second, the ice is undergoing a phase change from solid to liquid. When a phase change occurs, the temperature will not change until the phase change is completed. So the ice needs to completely melt before the temperature will rise.

With this information, here is a riddle. You are given a hot cup of coffee. You cannot drink it for two minutes. You want to add cold cream to your coffee. Which will give you the hottest cup in two minutes? Do you add the cold cream to the coffee and wait two minutes or do you wait two minutes and then add the cold cream?

#### jpanhalt

Joined Jan 18, 2008
8,767
Ice requires more heat to melt than to cool in the liquid state.

From Wikipedia:
When ice melts, it absorbs as much energy as it would take to heat an equivalent mass of water by 80 °C.

#### LesJones

Joined Jan 8, 2017
2,513
The quantity of heat required to change the state of ice into water is higher than to change the temperature of the same quantity of water from say 100 Deg. C down to say 20 Deg. C. To change the state of 1 gram of ice into water requires 80 calories. (Latent heat of fusion.) This is the same quantity of heat for 1 gram of water to chnge it's temperature by 80 Deg. C. The rate of heat loss will be about proportional to the difference between the temperature of the contents and the ambient temperature. So with the contents starting at 100 Deg. C you will have a differential of 80 Deg.C (assuming 20 Deg. C ambient.) With Ice the differential will be 20 Deg. C.

Les.

#### crutschow

Joined Mar 14, 2008
24,397
Do they really hold a vacuum between their inner and outer walls
Yes, they do.

#### cmartinez

Joined Jan 17, 2007
6,789
Ice requires more heat to melt than to cool in the liquid state.

From Wikipedia:
* slap in the forehead * ... darn! now I feel stupid... I had forgotten about the latent heat of fusion! ... and I'm an engineer! ... oh well, let's pretend this never happened.

And yet... even with no ice, cool liquids seem to last longer than hot ones... Considering Newton's law of cooling, I'd say that an experiment needs to be made using two identical cups, with identical amounts of liquid having a temperature difference vs ambient in opposite directions.... see which one reaches ambient temp first... but I'm willing to bet it will be the warm one.

#### cmartinez

Joined Jan 17, 2007
6,789
Yes, they do.
Now that is amazing ... I'd love to have a peek at their production process.

#### crutschow

Joined Mar 14, 2008
24,397
see which one reaches ambient temp first... but I'm willing to bet it will be the warm one.
You are on.

#### cmartinez

Joined Jan 17, 2007
6,789
You are on.
gee... thanks for the enthusiasm... I'll wait for you to report your results first, and then I'll let you know mine...

#### wayneh

Joined Sep 9, 2010
16,271
There are two things going on. First, the delta T for hot liquids is higher so you have a larger driving force. Coffee is brewed at 190 degrees F, room temperature is 68 degrees F, where as an iced drink is at 32 degrees F so the delta T is smaller for cold liquids. Second, the ice is undergoing a phase change from solid to liquid. When a phase change occurs, the temperature will not change until the phase change is completed. So the ice needs to completely melt before the temperature will rise.

With this information, here is a riddle. You are given a hot cup of coffee. You cannot drink it for two minutes. You want to add cold cream to your coffee. Which will give you the hottest cup in two minutes? Do you add the cold cream to the coffee and wait two minutes or do you wait two minutes and then add the cold cream?
Very good for a first post! I agree completely with your analysis, lower ∆T plus phase change.

As for the riddle, add the cream first. This reduces ∆T and therefore minimizes heat loss over the next two minutes.

#### jamiepatterson

Joined Apr 10, 2018
4
You are correct Wayneh. That was an interview question at a firm I once worked at. It was fun to watch the young interviewees figure it out.

#### jpanhalt

Joined Jan 18, 2008
8,767
I heat my cream and add it first. About 15 s in a microwave works about right, Of course, that might not work so well for a steel mug.

#### cmartinez

Joined Jan 17, 2007
6,789
Of course, that might not work so well for a steel mug.
I'm trying to picture the disaster of placing one of those things in a microwave...

#### joeyd999

Joined Jun 6, 2011
4,331
I heat my cream and add it first. About 15 s in a microwave works about right, Of course, that might not work so well for a steel mug.
For some reason, I like the fake dried soy bean powder so much more than cream. And it doesn't cool the coffee.

#### crutschow

Joined Mar 14, 2008
24,397
gee... thanks for the enthusiasm... I'll wait for you to report your results first, and then I'll let you know mine...
Sorry it's your experiment, not mine.
But there is a factor I haven't considered.
The hot liquid will cool from evaporation also, so that will skew the results towards the hot liquid cooling faster.
So you would need to use a liquid that doesn't evaporate appreciably, such as cooking oil.

Last edited:

#### cmartinez

Joined Jan 17, 2007
6,789
Sorry it's your experiment, not mine.
But there is a factor I haven't considered.
The hot liquid will cool from evaporation also, so that will skew the results towards the hot liquid cooling faster.
So you would need to use a liquid that doesn't evaporate appreciably, such as cooking oil.
Wouldn't the lid have an effect on that anyway? I mean, vapor will have nowhere to go if the lid is in place... Of course, all lids have tiny vent holes in them, and vapor pressure would never increase... so the vapor does have somewhere to go, after all...

#### jamiepatterson

Joined Apr 10, 2018
4
I have been trying the experiment with beer. The beer never seems to get warm. No matter how many times I try the experiment.

#### joeyd999

Joined Jun 6, 2011
4,331
Wouldn't the lid have an effect on that anyway? I mean, vapor will have nowhere to go if the lid is in place... Of course, all lids have tiny vent holes in them, and vapor pressure would never increase... so the vapor does have somewhere to go, after all...
Ahhh... but the humidity under the lid is as close to 100% as you can get in an unsealed environment, thus all but prohibiting additional evaporation.