Fri., Sep. 29 notes

Friday Sept. 29, 2006

There is an optional assignment due on Monday at the beginning of class. If you want to complete the assignment but haven't picked up a copy you'll be able to pick one up in PAS 588 next Monday before class.

The beginning of class was somewhat chaotic; none of the audiovisual equipment was working. We started covering the material on p. 45 in the photocopied class notes. I've taken that information and split it into two separate pages. When you add energy to an object, the object will usually warm up. Below we work out the equation that connects energy added and the resulting temperature change. The equation can also be used when energy is removed from an object. In that case the object will cool.

When you add energy to something the temperature change will depend on how much energy was added. So delta E is in the numerator of the equation. When you add equal amounts of energy to a small pan of water and to a large pan of water, the small pan will heat up more quickly. The temperature change, delta T, will depend on the mass. A large mass will mean a small delta T, so mass should go in the denominator of the equation. Different materials react differently when energy is added to them. A material with a large specific heat will warm more slowly than a material with a small specific heat. Specific heat behaves in the same kind of way as mass. Specific heat is sometimes called "thermal mass."

An object will usually warm when you add energy to it. But there is another possibility (mentioned at the bottom of the figure). The object could change phase. Adding energy to ice might cause the ice to melt. Adding energy to liquid nitrogen could cause the nitrogen to evaporate.

Here's an example that shows the effect of specific heat. Equal amounts of energy (note that calories are units of energy) are added to equal amounts of water and dirt. We use water and dirt in the example because most of the earth's surface is either water or dirt. Water has a higher specific heat than soil, it only warms up 4 C. The soil warms up 16 C.

I forgot to show the next figure in class. Because of different specific heats, land and water warm at different rates in the summer and cool differently in the winter.

Because of its proximity to the ocean, a city on a coast won't warm up as much during the summer and won't cool as much during the winter as a city that is further inland. In the example above City A has an annual range of temperature of 20 F, in City B there is a 60 F difference between summer and winter temperatures.

OK so you add energy to an object and the object warms. What is that increase in temperature telling you about what is happening inside the material?

Temperature provides a measure of the average kinetic of the atoms or molecules in a material. You can think of heat as being the sum total kinetic energy of all the molecules or atoms in a material. The next figure might make the distinction between temperature (average kinetic energy) and heat (total kinetic energy) clearer.

A cup of water and a pool of water both have the same temperature. The average kinetic energy of the water molecules in the pool and in the cup are the same. There are a lot more molecules in the pool than in the cup. So the total kinetic energy of all the molecules in the pool is going to be much larger than the total of all the kinetic energies in the cup. There is a lot more stored energy in the pool than in the cup. It would be a lot harder to cool (or warm) all the water in the pool than it would be the cup.

In the same way the two groups of people have the same average amount of money per person. The $100 held by the group at the left is greater than the $20 total possessed by the smaller group of people on the right.

You need to be careful what temperature scale you use. You must use the Kelvin temperature scale because it does not go below zero.

You should remember the temperatures of the boiling point and freezing point of water on the Fahrenheit, Celsius, and Kelvin scales. 300 K is a good easy to remember value for the global annual average surface temperature of the earth.

You certainly don't need to try to remember all these numbers. The world high temperature record was set in Libya, the US record in Death Valley. The continental US cold temperature record of -70 F was set in Montana and the -80 F value in Alaska. The world record -129 F was measured at Vostok station in Antarctica. This unusually cold reading was the result of three factors: high latitude, high altitude, and location in the middle of land rather than near or surrounded by ocean. You'll find more record high and low temperature data on p. 58 and p. 60 in Chapter 3 of the text. Precipitation records are shown on p. 348.

We did a short experiment in class (it was actually done at the end of class but I'm going to insert it in the online notes here)
The object of the experiment was to measure the latent heat of vaporization of liquid nitrogen. That just means measuring the amount of energy needed to evaporate a gram of liquid nitrogen. The students that are doing Experiment #2 are measuring the latent heat of fusion of ice, the energy needed to melt one gram of ice.

First we will make use of the Delta T vs Delta E equation (see lower left corner in the picture above). Rather than solving for Delta T we will rearrange the equation and solve for Delta E.

We poured 157.2 grams of water into a styrofoam cup and measured its temperature (23 C). Then we weighed out 31.3 grams of liquid nitrogen into a second cup and poured it into the cup of water (after having removed the thermometer). We waited until all the liquid nitrogen had evaporated and remeasured the temperature of the water.

It takes energy to turn liquid nitrogen into gaseous nitrogen. The needed energy came from the water. When energy is removed from the water the water cools. By measuring how much the water cooled and knowing how much water we had we can calculate how much energy was given up by the water. That is the 1729.2 calorie figure above. This was used to evaporate 31.3 grams of liquid nitrogen. So 55.2 calories was needed per gram. That is our measured value. The know value is 48 cal/g, so our measurement was reasonably close to the known value.

There are four energy transport processes: conduction, convection, latent heat and electromagnetic radiation. We only had time to look at one of these in class today.

The figure above illustrates energy transport by conduction. A hot object is stuck in the middle of some air. In the first picture the random motions of the atoms or molecules near the object have caused them to collide with and pick up energy from the object. This is reflected by the increased speed of motion or increased kinetic energy of these molecules or atoms (these guys are colored red). In the middle picture the energetic molecules have collided with some of their neighbors and shared energy with them (these are orange). The neighbor molecules have gained energy though they don't have as much energy as the molecules next to the hot object. In the third picture molecules further from the object now have gained some energy (the yellow ones). The random motions and collisions between molecules is carrying energy from the hot object out into the material.

The rate of energy transport depends on the material. Thermal conductivities of some materials are listed above. Air is a very poor conductor of energy. Air is generally regarded as an insulator. Water is a little bit better conductor. Metals are generally very good conductors. Diamond has a very high thermal conductivity. Diamonds are sometimes called "ice." They feel cold when you touch them. The cold feeling is due to the fact that they conduct energy very quickly away from your warm fingers when you touch them.

The rate of energy transport also depends on temperature difference. If the object in the picture had been warm rather than hot, less energy would flow or energy would flow at a slower into the surrounding material.

Here's a demonstration that we didn't do in class (this figure wasn't shown in class). If the instructor were to open a bottle of glacial acetic acid (acetic acid gives vinegar its characteristic smell) in the front of the classroom, the odor would eventually spread throughout the class room. This is an example of diffusion. The acetic acid molecules would be moved through the room by random collisions with air molecules. In many respects this is like the conduction of heat. The demonstration wasn't performed because the concentration of the acetic acid in the air, at least in the front of the room, would be high enough to present a serious risk to the instructor and students.