Effect of Sugar on Coffee Heat

[isaaclimdc]

Hi all,

I'm currently working on a lab on thermal physics, and I'm investigating whether adding different amounts of sugar is able to maintain the temperature of a cup of coffee, i.e. keep the coffee hot.

I have collected my results, and it turns out that more sugar keeps the coffee hot for a longer period of time.

Well my question is, what kind of analysis and conclusion can I make of results like that?

Thank you for your time,
Isaac Lim.

 

[Marco_84]

Hi all,

I'm currently working on a lab on thermal physics, and I'm investigating whether adding different amounts of sugar is able to maintain the temperature of a cup of coffee, i.e. keep the coffee hot.

I have collected my results, and it turns out that more sugar keeps the coffee hot for a longer period of time.

Well my question is, what kind of analysis and conclusion can I make of results like that?

Thank you for your time,
Isaac Lim.

You can check the thermal capacities between fluids and solid.
I think, I am not experimentalist, but knowing the amount of heat you gave to the system you can figure out this quantity also..

regards
marco

 

[isaaclimdc]

are you referring to the specific heat capacity?

cos this lab is meant to be about determining a practical factor that will help to keep coffee warm.

 

[tiny-tim]

Funding is an important part of physics!

I think you should contact some sugar companies and get them to fund your research!

You could become the acknowledged expert on the use of coffee in laboratories and other workplaces, and make regular appearances on chat shows.

If I were your PhD supervisor, I would suggest that you might also like to investigate how the note produced, when a teaspoon hits the side of the cup while stirring the sugar, changes as more sugar dissolves - I believe there was a paper published on this in Cambridge (England) in the 1960s, but I'm sure it could do with updating.

 

[isaaclimdc]

I think you should contact some sugar companies and get them to fund your research!

You could become the acknowledged expert on the use of coffee in laboratories and other workplaces, and make regular appearances on chat shows.

If I were your PhD supervisor, I would suggest that you might also like to investigate how the note produced, when a teaspoon hits the side of the cup while stirring the sugar, changes as more sugar dissolves - I believe there was a paper published on this in Cambridge (England) in the 1960s, but I'm sure it could do with updating.

i came to this forum for some help with IB physics. I am currently averaging 43/45 for my IB, so I'm not much of an idiot.

However, I am just looking for some ideas about useful conclusions to draw, so the sarcasm is not helping..

 

[pam]

The main heat loss for hot coffee is through the air at the top.
Cover the coffee cup and see if the effect persists.

 

[symbolipoint]

i came to this forum for some help with IB physics. I am currently averaging 43/45 for my IB, so I'm not much of an idiot.

However, I am just looking for some ideas about useful conclusions to draw, so the sarcasm is not helping..

Isaaclimdc might not be joking. Reasonable may be that someone may have studied thermal effects of sugar and hot water in some physically precise way.

Related to this; someone in conversation stated that one of the effects of using cream in coffee is that a thin layer of lipid or oil at the top surface of the beverage keeps in heat of the beverage - keeps the coffee hotter longer. True or not, try to actually make a measurement and find out.

 

[russ_watters]

The only factors here are the heat capacity of the sugar and the energy of the dissolution reaction of the sugar in the coffee. The data is freely available on the web and the calculations very straightforward.

 

[isaaclimdc]

Isaaclimdc might not be joking. Reasonable may be that someone may have studied thermal effects of sugar and hot water in some physically precise way.

Related to this; someone in conversation stated that one of the effects of using cream in coffee is that a thin layer of lipid or oil at the top surface of the beverage keeps in heat of the beverage - keeps the coffee hotter longer. True or not, try to actually make a measurement and find out.

You have a point with that one.. I will try to see whether that is applicable for the addition of sugar. Thank you for the suggestion.

The only factors here are the heat capacity of the sugar and the energy of the dissolution reaction of the sugar in the coffee. The data is freely available on the web and the calculations very straightforward.

How can I relate the energy of the dissolution reaction the sugar in coffee? I could show how the heat released contributes to the temperature of the system (coffee) right?

Thank you for your replies and taking me seriously.

 

[russ_watters]

Yes, any heat released (be sure the reaction is exothermic...) contributes to the temperature of the coffee.

 

[pchalla90]

Hey, i can't help much, but you may want to take a look at this:

http://demonstrations.wolfram.com/TheCoffeeCoolingProblem/

you're going to need to download the mathmatica player off to the right, as a button

you could also just use the online version, but you can't control it at all. i suggest downloading both player and document.

off topic: there are other really cool physics and other documents on there to look at.

 

[isaaclimdc]

Okay that is a great idea. Thank you.

 

[pchalla90]

another factor to consider

do you know the law of cooling and heating?

in case you don't, it states that

the change in temperature over the change in time is proportional to the difference between the temperatures of the liquid and of the environment.

basically it states that

dT/dt=k(T-T(s))

where:
T is temperature
t is time
T(s) is the temperature of the surrounding environment
and k is a constant that is specific to the liquid.

remember that T(s) is a constant and not a variable.

it comes out to

T=Ce^(kt)-T(s)

you need to know a couple things before figuring out c and k. you need to know the temperature at two different times, one preferably being at t=0

first plug in t=0, so that k doesn't matter, then e^0=1. you have and equation with one variable, C. solve for c. then go back and use the other temperature and time to solve for k.

then it will work for every time you plug in. make sure you keep all units constant. it doesn't matter whether you use hours or minutes or Fahrenheit or Celsius. as long as the next time you go and plug into the solved formula, you use the same units.

see if that helps.

 

[isaaclimdc]

Wow that's a little complex.. but I follow it. However, how can I relate this to the sugar situation?

 

[Bystander]

(snip)I have collected my results, and it turns out that more sugar keeps the coffee hot for a longer period of time.
(snip)

1) This is homework. You don't make a stab at the conclusions, you don't get help.

2) Expand "collected my results," and you'll give yourself a few things to think about, as well as giving people enough information to help you.

3) "IB?" Maybe it's well enough designed to "just follow directions," and maybe it's deliberately a poor design to make you think about "the scientific method."

4) Pam's given you a hint, Russ has commented on heat of solution, and you've been handed the cooling law on a platter; your "collected results," as described, lead you no where near the cooling law, nor anything concerning heat of solution.

Think about how you would describe the "experiment," background, procedure, and results.

 

[pchalla90]

i agree with bystander in saying that if you post your data and results on here, it would be a great help to all of us...

if you looked carefully at the mathmatica document, it showed that adding something at room temperature would cause the cooling rate of the liquid to slow down. the other cup shows that if you don't add it in at all, it'll cool quicker.

what conclusion can you make from that? how does it relate to your problem?

 

[isaaclimdc]

Sorry, but how can I quantitatively relate the specific heat capacity of sugar into explaining why it is able to keep the coffee warm for a longer period of time??

Do I say that total Q = Q of coffee + Q of sugar?

Thanks.

 

[pchalla90]

The law of cooling states that when objects are hot, they will cool faster than if they started at a lower temperature. If you graph T=Ce^(kt)+T(s), you'll notice that as time goes on, the rate of cooling slows down. That's obvious. But if you started it at a lower temperature, it won't cool as fast as the one that's at a higher temperature.

How does that relate to your question?

When you have pure coffee and no sugar, the temperature is higher than if you had coffee with 1 part sugar, which in turn is higher than 2 parts sugar.

See what I'm getting at?

The temperature that you're starting at for pure coffee is high, so as I said before, it'll cool the fastest.

The temperature that you're starting at for coffee plus 1 part sugar is slightly cooler than pure coffee, so it'll cool slower than the pure coffee.

The temperature that you're starting at for coffee plus 2 parts sugar is still slightly cooler than 1 part sugar, so it'll cool slower than both the above scenarios.

That's what the "Coffee cooling problem" link that I posted awhile back shows.

Other than that, I don't know how else to help you.

 

[isaaclimdc]

The temperature that you're starting at for coffee plus 1 part sugar is slightly cooler than pure coffee, so it'll cool slower than the pure coffee.

The temperature that you're starting at for coffee plus 2 parts sugar is still slightly cooler than 1 part sugar, so it'll cool slower than both the above scenarios.

But why does adding sugar make it start out cooler initially?

 

[pchalla90]

because the sugar is at room temperature and the pure coffee isn't... the temperatures have to come to equilibrium, so heat is taken from the coffee and given to the sugar. the temperature has to decrease to increase the temp of the sugar.

i'm thinking along the lines of the link i posted awhile back. go look at that again.

 

[tiny-tim]

"On note emitted from a jug while mixing instant coffee."

I believe there was a paper published on this in Cambridge (England) in the 1960s, but I'm sure it could do with updating.

I've found it at last: it's in the Proceedings of the Cambridge Philosophical Society, volume 65, page 365 (1967).

The authors are Farrell W.E. (whose usual field seems to be plate tectonics), Mackenzie D.P., and Parker R L, and the title is:

On note emitted from a jug while mixing instant coffee.​

I checked it in Science Citation Index, and found that no-one seems to have cited this work (at least, up to 1984 - at that point, I decided my coffee was getting cold, and gave up looking) - so you could be the first person to do so!

Unfortunately, my library has no volumes before volume 77, but from memory they discovered that the note depends on, and changes with, the density of air molecules trapped against the coffee grains.

Well … it was the sixties … and that sort of thing was important …