Jump to content

Thermal Dynamics question.


thorne

Recommended Posts

Ok, So I've thought over and over about this and i just can't figure out which i think would happen first.

 

 

So here is the scenario.

 

You have a room temp of 70c

you have a cup of water at 65

you have a cup of water at 75

 

Which will reach room tempture first and why. Would it be the same answer if the amounts from room tempture were equal but greater so.

 

85 and 55.

 

 

I know there is someone on here that could answer this question correctly.

Link to comment
Share on other sites

The hotter cup.

 

The room has more mass of average temperature than the liquids. By design, molecules want to move faster within their realm of energy, so they "steal" heat to increase their movement, thus why things cool down.

 

The room has a greater mass than the cup of cooler liquid, so the room's mass will steal the heat from the hot liquid of smaller mass, cooling it down quicker than a small mass cup of liquid trying to steal the heat from a room much bigger than itself.

Link to comment
Share on other sites

It will take longer to get make the cool water warmer. Not sure exactly why, but think about it, heat rises and leaves the cup. The cooler water will be somewhat insulated and liquid, esp water holds its temp well. Thats my guess, I think I'm right just not sure how to explain it...

 

 

Edit: OK, I fail at being smart enough to know why, but I did know the hot cup would cool faster :)

Link to comment
Share on other sites

I did and I disagree.

 

Newtons Law of Cooling:

dT/dt = -k(T-Ta)

 

"k" is the thermal barrier constant thingy, which will be the same for both cups in this case. There is no mass relationship in this equation, just a temperature differential across the thermal barrier.

 

If you don't belive me, just plug in the numbers, integrate each with respect to "t", and plug in the same time for each. I would, but I don't have my calculator and I suck at calculus without it (I suck at calculus anyways though).

Link to comment
Share on other sites

From wikipedia:

 

The second law of thermodynamics is an axiom of thermodynamics concerning heat, entropy, and the direction in which thermodynamic processes can occur. For example, the second law implies that heat does not spontaneously flow from a cold material to a hot material, but it allows heat to flow from a hot material to a cold material. Roughly speaking, the second law says that in an isolated system, concentrated energy disperses over time, and consequently less concentrated energy is available to do useful work. Energy dispersal also means that differences in temperature, pressure, and density even out. Again roughly speaking, thermodynamic entropy is a measure of energy dispersal, and so the second law is closely connected with the concept of entropy.

Link to comment
Share on other sites

The hotter cup.

 

The room has more mass of average temperature than the liquids. By design, molecules want to move faster within their realm of energy, so they "steal" heat to increase their movement, thus why things cool down.

 

The room has a greater mass than the cup of cooler liquid, so the room's mass will steal the heat from the hot liquid of smaller mass, cooling it down quicker than a small mass cup of liquid trying to steal the heat from a room much bigger than itself.

 

you beat me to it

 

same reason hot water freezes faster then cold water

Link to comment
Share on other sites

Ummmm, dood, you are still agreeing with me. When the cup is hotter than the room, the heat flows from the cup to the room. When the room is hotter than the cup, the heat flows from the room to the cup.

 

According to Newton, it will take the same amount of time to do either.

 

 

 

They will both take the same amount of time to reach room temperature, and a bigger variation will not change this.

Link to comment
Share on other sites

heat does not spontaneously flow from a cold material to a hot material, but it allows heat to flow from a hot material to a cold material

 

The way I understand it, the heat from the room will not flow too the cold water as fast as the heat from the hot water will flow to the room.

 

I could be wrong, I am far from an expert when it comes to this kind of thing.

 

I might have to setup a 5th science class style experiment in my kitchen just to know for sure

Link to comment
Share on other sites

Um not a single person yet nailed the OTHER difference between hot and cold water? VAPOR PRESSURE. Given a temperature and a pressure, a given material has a prescribed rate of vaporizing (helpful hint, the rate increases as the temperature increases). This means that the hotter cup will vaporize (and in doing so give up energy) at a faster rate than the cooler cup. Of course, it also depends on the ambient temperature and humidity of the surrounding air.

 

The other factor that you have to consider is the convection of air vs. water. Given that both cups are made of the same material, the cooler cup will cause a downward convection current in the air and an upward convection current in the water. The warmer cup will do the opposite. What you forgot to ask was: What shape are the cups!

 

Answer that and you will be one (of many) steps close to a conclusive solution to this problem.

 

Here's another question: Did you really mean 70c? If that's the case, and the air is relatively dry, then your two cups may be completely void of water before they both reach the same temperature.

Link to comment
Share on other sites

^True, but since he did not give wet bulb temps, dry bulb temps, barometric pressure, relative humidity, cup composition, purity of the water, size and infiltration rates of the room, position of windows and time of day/season... well, fuck, you could go on all day! He also doesn't say wether the cup is sealed or not; it might be a thermos.

 

I doubt he is trying to split hairs that finely ;)

Link to comment
Share on other sites

I doubt he is trying to split hairs that finely ;)

 

The philosophy of physics is indeed to split hairs until there is nothing left ;)

 

This is clearly evidenced in the overwhelming majority of threads here on CR.

 

Oh yeah, I went there.

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...