Science Buddies: "Ask an Expert"

I have found that covering a cup of hot water with a cover made from silver building paper kept the temperature of the water hotter than a cup of hot water in an uncovered cup. i measured the water temperature in both cups every 2 minutes for 30 minutes. Can you please explain why insulating and covering the cup keeps the water from cooling down.

Hannah:

When two objects of differing temperatures come in contact heat will be exchanged, and it will flow from the warmer to the cooler object.

How quickly the heat transfer occurs depends on the specific heat of the materials. Specific heat is defined as the heat required to change the temperature of a unit mass of a substance one degree.

The uncovered cup has no barrier to heat exchange with the air. The silver building paper must be heated before it begins to transfer heat to the air thus the water beneath the silver building paper stays hotter than the water in the cup.

Matt Mulanax

MY DAUGHTER IS DOING A PROJECT ON HOT AND COLD WATER IN CUPS. MY QUESTION IS WHICH CUPS ARE BETTER FOR INSULATION AND WHY?

There are two basic aspects of a cup that control how well it keeps it's contents cold or hot. The material the cup is made out of and it's thickness.

In general the denser the material is, the better conductor of heat it is and the worse insulator it is. The reasoning behind this is that heat travels via the vibration of molecules and atoms, so with fewer molecules it's hard for heat to move through a substance (that's a really big simplification). So metals (which are very dense) tend to conduct well while lighter materials (like styrofoam) tends to be better insulators. A thermos is a double walled bottle, with a vacuum (nothing, almost no air) inside as this makes an excellent insulator. You can look up "aerogel" to read about the stuff NASA has been using for insulation.
Thicker cups tend to be better than thinner cups. As it takes longer for heat to travel through the cup and to the outside air.

For more information try looking up "heat", "heat conductance", "first law of thermodynamics", "thermos", "aerogel" and you will get a longer and probably better explanation (wikipedia.org has some quick summaries as well).

WHAT IS THE BEST WAY TO TELL HOW WELL STYROFOAM CUPS INSULATE HOT AND COLD WATER COMPARED TO PAPER CUPS? PLEASE HELP US WITH THIS!!!!!

The correct answer to the first question of why a thin silver builder's paper served to slow the heat loss is as follows:

Heat does indeed flow across a temperature gradient, and specific heat does indeed determin how fast a material's temperture will rise with a given heat flow into the material.

However, the builders paper is thin and would heat up quite quickly to the temperature of the air below it inside of the cup. Why? Because of water condensing on the inner surface carries and transfers a great deal of heat as it evaporates off of the hot water travels through the air by convection currents as water vapor where it condenses back to water. This phase change has very high latent heat energy. Keywords: "phase change" and "Latent heat of vaporization". Search on these terms.

So, if the heat is very quickly transfered to the paper or foil, which comes to thermal equillibrium very quickly do to its low mass compared to the high latent heat transfer... then why does it slow the cooling of the water?

Answer: Because the high thermal flux transfer path, the water vapor excaping the open mouth of the cup, has been cut off. Now, the heat must transfer across the builders paper. Paper is a fairly good thermal insulator, but the real slowdown is from the relatively slower heat transfer to the dry air just above the foil. This must then be carried away by convection currents... and it is THIS material that has a low specific heat, so that for a given amount of convection, less heat is carried away then would happen with the moisture laden air from inside the cup.

The second question, what makes a good thermal insulator as opposed to a poor one... or to reverse the question, what makes a good thermal conductor as opposed to a poor thermal conductor... conduction and insulation are two sides of the same property, mathematic the inverse of each other.

What makes a good thermal conductor is strong molecular bonds in very regular order. What makes a poor thermal conductor (a good insulator)? Weak molecular bonds with disordered arrangements... Why? Because heat is transfered in a material by the vibration of the atoms... and strong bonds cause the neighboring atoms to vibrate with them... while disorder, jumbled up bonds or atomic arrangments cause the vibrations, sounds (in the world of the small, energy is quantized to behave like particles, so the sound energy "particles" are called "phonons" another Keyword to search on) to literally bounce and around and scatter like the steel balls in a pinball machine, slowing their travel through the material.

Notice that strong bonds and regular order is important, NOT density! Stainless Steel is much denser than a diamond... since a diamond is made of the relatively light material carbon... but a diamond has very, very strong bonds... which is why it is the hardest material we know of... and it is a very regular arrangement, called approapriately, the diamond cubic arrangement. Now, it probably wouldn't surprise you that a diamond is the best thermal conductor ever measured. Other materials have this same arrangement, like silicon used in making computer chips... also a relatively light material... but it too is far more thermally conductive than stainless steel. So why is stainless steel relatively poor at conducting heat? Because it is an allow of several different kinds of atoms... which causes it to be irregular in its atom arrangements on a small local scale... and thus cause the phonons to bounce around.

What makes a styrofoam cup so poor as a thermal conductor, and thus a good thermal insulator? Why... because it is "inhomogenous"... that it is full of holes! It has microscopic holes filled with air. Air is not a good thermal conductor because it has very low bond strength... in fact, it is a gas... and thus as NO bond strenth... and it is randomly arranged... and thus bounces the heat, just as the gas molecules themselves bounce around.

So there you have it.

Now... how to measure which materials make good thermal insulators for constructing a cup for hot water? I think you already know the answer... put in hot water a known temperature in a colder environment and measure how fast the temperture drops. One way would be to put the cups in a cold water bath. That way, the environment is uniform and a fairly good heat sink.

Good luck with the experiments.

I ASKED THE WRONG QUESTIONS. WHICH MATERIALS ARE THE BEST INSULLATION FOR HOT AND COLD WATER?WHAT IS THE BEST WAY TO CHECK THIS? MY DAUGHTER IS IN THE 5TH GRADE AND SHE HAS TO DO A WHOLE PRESENTATION WITH PROOF AND WHAT NOT.PLEASE HELP US ON THIS!

Roccod,


The most straight forward way for a 5th grader is to use cups of the same size. Pour in a measure amount of hot water, so that the same amount of water goes into each cup. Put on lids, if available. Place the cups in a cold water bath... a large pan or tub... large enough so that the water in it is many times larger in volume than the water in the cups. measure the water temperture over time. The heat transfer will cause the hot water to cool. If there is a difference in the cooling rate, it will be directly proportional to the thermal conductivity of the cups.

Note that thermal conductivity/resistance is almost exactly analogous to electrical conductivity/resistance. What I proposed above is like a capacitor with a given voltage being discharged to ground through an unknown resistor. The time it takes to discharge is inversely proportional to the electrical resistance.

In the case above, you will not get an absolute number for the thermal conductivity/resistance, but you will get relative numbers for cups with differing materials.

Good luck.

The purpose of insulation is to slow down the flow of energy. When energy leaves the water in the cup, it cools off. Simple as that. The insulation means it takes longer for the energy to leave the water.

In the case of hot water, there is a second mechanism involved. The evaporation of water from the surface. Covering the cup slows the evaporation process as well.

A third mechanism of insulation is that when the water vapor (from the evaporation) condenses on the cover, the vapor cools and the cover is warmed. If the cover conducts heat away rapidly, more vapor will condense. If the cover insulates, the surface of the cover will stay hot and reduce the condensation and the loss of energy.

A fourth mechanism is that the cover prevents convection flow. Regardless of evaporation, convection will circulate hot air away and bring cool air towards a hot object. The cover prevents this.

So much for the free answers. Now, you need to do some work. Make a container with two inches of styrofoam on the sides and bottom, so that all the heat will go out the top. Experiment with different covers. None, aluminum foil, cardboard, and thick styrofoam. Report the rate of heat loss for each and correlate that to the insulation properties of the cover material.

Robert Reavis

THANK YOU ALL!!!!! MY NEXT QUESTION IS ABOUT PLASTIC CUPS. HOW DO WE CHECK THIS OUT? COMPARED TO STYROFOAM AND PAPER CUPS!

ROCCOD wrote:THANK YOU ALL!!!!! MY NEXT QUESTION IS ABOUT PLASTIC CUPS. HOW DO WE CHECK THIS OUT? COMPARED TO STYROFOAM AND PAPER CUPS!

Keep it simple, but think what you are trying to measure.

Get styrofoam and paper\ cups that are the same size (inside) and shape.
Pour in equal amounts of water at the same temperature.
Cover.
Wait tem minutes.
Measure the two water temperatures.

You explain:
Why the same size and shape is vital.
Why the same amount of water is vital.
Why a cover is vital.
Which is the better insulator, and why.

ROB,WITH ALL RESPECT,HOW DO I ANSWER THE 1ST 3 QUESTIONS? I AM NOT GOOD AT THIS SCIENCE STUFF

ROCCOD wrote:ROB,WITH ALL RESPECT,HOW DO I ANSWER THE 1ST 3 QUESTIONS? I AM NOT GOOD AT THIS SCIENCE STUFF

ROCCOD, in science we want to have "controlled" experiments. By that I mean we try to identify all the possible "factors" that might affect our results and "control" all of them to be the same, except for the experimental factor. For example, one factor that affect the temperature of your cup is the environment.

For instance, if you put one cup in the freezer, and one cup in the oven... obvious the temperature of the water in the cup will be affected. So the temperature of the air around the cup is a "factor." Since you are testing paper vs styrofoam, you want to "control" this factor so that it is the same both for tests... otherwise you don't know if the water stayed warmer in the cup because of the material the cup is made out of, or because something else you did.

Similarly these following three "factors" must be controlled.

1. Size and Shape of the Cup
2. Amount of water
3. Cover

Each of these factors would affect how the termperature of the water would change if they were different. As mentioned previously, the water loses heat to the air from the top of the cup, to "control" this you want to put the same type of cover on both cups so that the heat lost is mostly through the cup itself (same idea as why you zip up your coat when it's cold out). Similarly, using different shaped/sized cups to also affect the experiment (think of how long it takes to boil a small pot of water versus a big pot of water).

The reason you need to explain these things is because if you don't properly control all the other "factors" you might get bad test results.

I hope this helps a little.

P.S. Try not to write in all CAPITALS. It's difficult to read.

What is the secret to science? My mother-in-law summed it up very nicely, she said, "Bob, now I know why you wanted to be an engineer, you are lazy." She was right too.

When you have problems involving many variables it gets very complicated very fast if you have to contend with more than one variable at a time. The temperature of the water indicates how much (thermal) energy is contained in the water. You lose energy when the heat goes out through the cup and the lid. Confine the differences to the lid.

Consider a cup with one shape compared to another cup with a different shape. As the shape changes, the ratio of volume to area changes. Heat loss depends on area. (Spread it out so it cools faster, remember?) Keep the size and shape the same and vary the lid's insulation only.
Since surface area relates to the square of the change while volume relates to the cube of the change, changing the amount of water (the volume) affects the cooling rate because you are changing the area to volume ratios. So, keep the area to volume ratio the same, use the same size cup and the same volume of water.

Cooling rates are also affected by the difference in temperature. Obviously the freezer will cause the water to cool faster because there is a bigger temperature difference. So, keep the outside temperature the same for all experiments and start with the same initial water temperature.

Cooling rates are affected by the material the heat is traveling through. A paper cup will probably cool faster than a styrofoam cup. So, do not change the cup material.

To measure the cover's effectiveness, change only the cover. Do not change the cup size, cup shape, cup contents, cup insulation, cup anything else, etc. Change only the cover. Repeat, change only the cover. Now, you say it... Change only the cover.

Keep it simple, it is easier that way. I am serious about changing only one variable and I am not trying to talk down to you. This problem is very simple if you keep it simple. Change only one variable, the lid.

Robert Reavis