In this section, we will discuss the first and second laws of thermodynamics. These two laws delineate the basic functions of all of the engines in our everyday life. They also describe the function of refrigerators, air conditioners, stoves, etc. In fact, we will find that they even characterize the basic functions within our body. These two laws describe how energy gets used and transferred from one form to another. The following experiments and activities can be found in this section.
Before we go any further, we need to define just what energy is. Technically, it is defined as "the ability to do work". This really does not seem to say much, since we have not defined work. For constant forces, work is defined by the equation W = Fxd, where F is the constant force and d is the distance through which the force is applied. Let us compute the work done for f raising some common objects. In the case of raising objects, the force involved is F = mg, where m is the mass of the object and g = 9.8 m/sec2.
Object Raised Mass Distance Work in Joules
Book, off floor to table _____ 1 meter __________ 500 gram weight _____ 1 meter __________ Child, off floor _____ 2 meters __________ Yourself, up stairs _____ 5 meters __________ Yourself, up Stone Mt. _____ __ meters __________
What is the consequence of the work that you do in these examples? You have given the objects energy. In fact, the work that you do is equal to the change in the energy of the object (W = E). In the case of lifting things in the air, you have given them gravitational potential energy. If you were to release them (please, do not drop the child), they would convert this potential energy into another form of energy. Let us look at a few examples of energy transfer.
For this experiment, we will need a paper cup, a marble or small ball, scissors, a long surface with a slotted groove (i.e., ruler with center groove), and ring stand. Cut a square section from the top of the cup large enough to fit the ball through it. Lift one end of the board with groove 1 cm and support it with the ring stand. Place the cup at the end of the groove with the cut out section directly facing the groove. Mark its position. Place the ball on the track and measure its height above the ground. Release the ball. What happens? Measure the distance that the cup is moved backward. Move the track up to 2 cm high and repeat. Keep doing this until the track is 10 cm high. Plot the distance traveled by the cup versus the height of the ball. What can you conclude?
This experiment is an example of potential energy. Because of its height relative to the ground, the ball has an amount of energy equal to mgh, where m=mass of the ball, g = 9.8m/s2, and h = the height of the ball. As the ball is released, the potential energy of the ball is converted to kinetic energy (energy of motion) as the ball decreases its height. When the ball reaches the bottom of the track, all of its potential energy has been converted to kinetic energy. The ball then hits the cup, where the ball gives some of its kinetic energy to the cup. However, due to frictional forces between the cup and the ground, the kinetic energy of both gets converted to heat.
Evaluation: This experiment received enthusiastic support of the participants. The experiment was easy to perform, the principles involved were easy to understand, and the data analysis presented an excellent opportunity to introduce graphing.
Another display of energy in action is the ballistic pendulum. The safest and most repeatable way to do this experiment is with one of the commercially made devices. However, these can be quite expensive to purchase. This experiment can be done in a homemade fashion with a block of wood on the end of a string and a small caliber rifle. This method is very UNSAFE and not recommended. For a safe version of this experiment, we will need a rubber band, a ring stand with a ring support, a board with 2 hooks, string, a small block of wood hollowed out on one side and 2 hooks attached on top, a piece of construction paper, a ball of clay, and a paper clip. Assemble the components as in the picture. The paper clip should be inserted at the top through the construction and should be free to swing 90 degrees about that point. The bottom end should stick out to catch the string as it is moving backward, and it should stay at the angle of highest ascent for the block so that measurements can be made. Mass the block before it is put in place, as well as the piece of clay that you are using. Place the clay next to the rubber band, pull back (measuring the distance that you have pulled it back), and release (make sure that the clay goes into the hollowed out portion of the block). Measure the angle of highest ascent. Repeat this procedure at ten different distances of pulling the rubber band back. Make a chart of the distance the rubber band was pulled back vs. the gravitational energy of the block and clay.
As opposed to the previous experiment, this experiment has potential energy stored in the rubber band. This potential energy is converted into kinetic energy when we release the clay. When the clay hits the block, it loses some energy to internal heating and transfers some to the block of wood. This combined kinetic energy then gets converted into gravitational potential energy.
Evaluation: This experiment was not performed. However, it was discussed by the particpants. It was decided that this type of experiment could present problems in some classroom settings. Even though clay is being used, it is still a projectile and could be used for mischief, if not injury.
As we saw in the previous two experiments, sometimes usable energy is lost when it is transferred. In the first experiment, it was lost due to friction between the cup and the table. In the second, it was lost to internal friction in the clay and wood during the collision. Let us look at a measurable example. For this experiment, we will need several different types of bouncing balls (ex. tennis ball, racquet ball, basketball, ping pong ball, superball, etc.). When we drop these balls, they do not return to the same height. Before we drop them, they have potential energy = mghi. After they bounce and come back up, they have potential energy = mghf. The energy lost = mg(hi-hf). Make a chart of the initial and final heights of a set of balls, calculating the amount of energy lost in each ball. Which ball performed best?
Evaluation: This experiment went well. The participants found that the supposed "Superballs" that they had actually lost more energy than the golf ball.
In the previous three examples, the usable energy lost went into waste heat. If you were to drop any one of the balls (especially the "dead" ones) enough times, you would begin to notice a temperature rise in the ball. This temperature rise is due to the heat generated by internal friction. It was not until the 1800's that a scientist by the name of James Joule recognized heat as a form of energy and quantified its production and use in an equation. This equation, known as the First Law of Thermodynamics, states that E = W + Q where E is the change in the energy of the object, W is the work done ON the object, and Q is the heat ADDED TO the object. This equation governs how energy can be transferred and used. For instance, the energy of a system can increase either by doing work on it or adding heat to it. The following activity shows the first situation.
Place a rubber band on your forehead and note its temperature (You can use any part of your body, but the forehead is very sensitive to temperature changes.). Stretch the rubber band with both hands, and then quickly place it against your forehead. What happens? By stretching the rubber band, you had to apply a force through a distance, i.e., you had to do work. Some of that work went into changing the potential energy of the band while some went into heat. This added heat changed the temperature of the band.
Evaluation: The participants found this demonstration enlightening. They were pleased that you could show that the rubber band could get cooler than air by stretching it, then letting it cool, and, finally, letting it return to its normal shape.
Now let us look at an example where heat is input and work is done. For this experiment, we will need a test tube, a balloon, two ringstands with holders, a small flat piece of wood or metal, a small weight (less than .2 kg), and a Bunsen burner/alcohol burner. Stretch the mouth of the balloon over the opening of the test tube and secure, if necessary, with a rubber band. Attach the test tube to one ring stand in a horizontal position at a height that is greater than the burner. Place the second ringstand near the first. Attach the flat piece of wood or metal to the stand at a height equal to the test tube's. Place the balloon on the flat piece and put the small weight on top. Start the burner and gently heat the test tube (Do not get flame near balloon). What happens?
As the test tube gets heated, the air in it expands. This causes expansion in the balloon, which raises the weight. In other words, the heat added to the system changed the internal energy of the system (the air went up in temperature) as well as doing work. This is the same process that occurs in an internal combustion engine. There, the gas is ignited (heat added), causing the temperature of the gas to increase (change in energy) and expand back against the piston (work done).
Evaluation: Not Done.
So far, all of our energy exchanges have involved heat in some way. Sometimes, we can have energy exchanged without heat being lost or added. Such a process is called adiabatic. An example of such a process can be shown with an old tire inner tube and a bicycle pump. First, pump the inner tube up to maximum pressure. In doing so, you should note that the inner tube becomes warm. Why is this? Allow the inner tube to sit for a while until it reaches equilibrium with the room (i.e., it is at room temperature). After several minutes, release the air in the inner tube against a sensitive area of your skin (ex. cheek, forehead, etc.). How does the air feel? The air feels cool because it has lost internal energy (temperature) as work is done by the system to accelerate the air as it comes out of the opening.
Evaluation: Not done.
That does not make sense, you say, because heat and temperature are the same thing or are at least related, right? The answer is no and yes. Heat is technically defined as "the energy transferred between two objects of different temperature" while temperature is defined as "the property that two objects have in common when no heat is being transferred between the objects". Circular definition, you say. Yes, but it is necessary. Heat is energy; in fact, it is energy that is transferred. No object can contain heat since heat is energy that is being transferred. Temperature, on the other hand, is a property of matter; it is not energy. The particular property that it is the one that objects have in common when no net energy is being transferred between them.
This makes sense when you consider what a thermometer is. For example, take an alcohol thermometer and place it in a bath of ice water. Does it read the correct temperature right away? No, it takes a while for the thermometer to reach the correct temperature. What is happening while it is making its way? When you first stick the thermometer into the ice bath, the thermometer has a higher temperature than the bath. Therefore, heat begins to flow out of the thermometer and into the ice bath. As it does, the internal energy of thermometer decreases, and the alcohol begins to contract. When the thermometer has reached the temperature of the ice bath, no more heat is transferred between the two systems, and the alcohol quits contracting.
The alcohol contracts, as do most substances, because it has a positive coefficient of volumetric expansion. This coefficient is defined as the fraction volume expansion per degree temperature change, i.e., thermal expansion coefficient = (V/V)/T. In fact, we can calculate this coefficient for alcohol from the thermometers. The total volume of the thermometer's inner tube is equal to LA where L is the length of the thermometer tube and A is the cross sectional area. For these thermometers, A = .12 mm2. The change in volume for a given temperature difference is just the distance between the temperatures (L) times the cross sectional area A. Most of the volume of alcohol in the thermometer resides in the bulb. Using a micrometer, estimate the volume of the bulb. Measure the distance between any two temperatures. Calculate the coefficient of thermal expansion using the number above and these measurements. Compare to the value of 1.1 x 10-3 K-1 figure for ethanol.
Evaluation: Discussed, but not done.
As we saw in the last demonstration, heat can be transferred by several methods. Actually, it can be transferred by three methods: conduction, convection, and radiation. Conduction is heat transfer by actual physical contact (ex. you touch a cold glass; heat gets transferred from your skin to the glass). Convection is heat transfer by material movement and mixing. It can either occur naturally (hot air rises) or by force (fan). The last form of heat transfer is radiation, which is the transfer by electromagnetic waves. An example of this is sunlight. The following experiments show these three methods.
Experiment 1: For this experiment, you will need two soda cans, insulating material, hot water, and two thermometers. Wrap one of the soda cans with insulation around the sides and bottom. Carefully, pour hot water into each can until the water is about 1 cm from the top (be sure not to get the insulation wet). Place a thermometer into each can and take a measurement. Continue to take measurements every minute for about 20 minutes. Plot temperature versus time. Which can retained the heat the best?
Evaluation: The experiment showed the differences between insulated and uninsulated very well when the hole was well sealed (stuff paper in the hole to help the rubber band seal it). When the hole was not well sealed, the difference was quite small. A glass coozy makes an excellent insulating material. Some discussion about safety (hot. scalding water in the cans) ensued.
Experiment 2: Using the same setup as in the previous experiment, remove the insulation from the one can. Refill each can to within 1 centimeter of the top with hot water. Place one of the cans in front of the fan and insert the thermometers. Again, record the temperature every minute for 20 minutes. Plot temperature versus time. Evaluation: Not done.
Experiment 3: Remove the water from the cans of the previous experiment. Spray paint one of the cans black and one of them white. Again, fill with hot water and insert the thermometers. Take readings every minute for 20 minutes. Plot temperature versus time.
Evaluation: The difference between the two cans' temperature was quite small (a degree or two after 15 minutes). Previous experience shows this to occur often. Testing the cans' absorptive abilities was discussed as a better option (difference between the temperatures is greater).
Of all of these experiments, which can lost heat the fastest? Which the slowest? Discuss.
Now that we have seen how heat can transferred, a good question to ask is "For what purpose can it be used?". As it turns out, heat transfer is the basis for almost every engine known to people. Almost every energy source we have is used to generate heat. The heat is transferred into either a gas or water. If it is put into a gas, the gas expands and pushes back a piston. If it is put into water, the water eventually boils, produces large volumes of steam that push back pistons or turbines. In either case, we use the heat generated by "burning" fuels to cause fluids to expand.
As we saw with the vinegar and baking soda, expanding gases can produce a good deal of propulsion (work). For this experiment, we are going to use a different expanding gas to produce propulsion. We will need balsa wood, scissors, copper tubing, small candles, long tray of water, and caulk/glue. Cut the balsa wood to make the bottom of a flat bottom boat (Remember, you might want to consider some hydrodynamics.). Cut sides to fit the bottom and either glue or caulk them in place (If you used glue, seal the glue with wax or caulk.). Bend the tubing back on itself such that there is one loop in the middle. Cut two small holes in the back of the boat big enough to put the tubing through. Put the tubing through. Prop the loop up with a small piece of wood or the candle. Fill the loop with water. Place the candle under the loop and set the boat in the water at one end of the tray. Light the candle and time the boat to get to the other end of the tray. What is the boat's motion? Calculate the average velocity of the boat. Take the tubing out and make another loop. Put it back in the boat and seal against leaks. Fill the tube with water, place the boat in the tank, and light the candle. Calculate the velocity again. Repeat for as many loops as you can get. Is there any difference in the speed of the boat? Why are why not?
Evaluation: The participants got the most fun out of this experiment. They were very enthusiastic about racing their boats. Caveats: The small tubing led to very small propulsion forces. A greater force could be achieved with a larger boiled volume. It would be best to try this experiment with a boiling chamber with attached pipes that go into the water.
Efficiency and the Second Law
In the last experiment, we saw that the input of heat into a system produced work (Since the water in the tubing was always boiling, the internal energy of the system was unchanging.). However, if we were to measure the amount of heat that was output by the candle and the amount of work produced, we would find that the two were not equal. Why is this? An answer to this question would be found if we could very accurately measure the temperature of the water in the tank and the air in the room. We would find that some heat was lost to the surroundings (ex. the steam being ejected out of the tube). This is known as waste heat, and it affects the amount of useful work that we can get out of our engine; the more energy that goes into waste heat, the less energy there is available to do work. We define the efficiency as the amount of useful work or energy output divided by the total amount of energy input. Ideally, you would want the efficiency of any engine to be 100%. However, the Second Law of Thermodynamics says that you can never have a 100% efficient energy conversion, i.e., there must always be waste heat (Actually, it states "In a closed system, the total entropy will always increase or stay the same". However, a result of this is the previous statement.).
Let us measure the efficiency of an engine. In the last experiment, we boiled water (input energy) in a small tube to drive (output kinetic energy) a small boat. The amount of energy that we input is approximately
Q = m x (4.18 J/gm oC) x (100 oC - Twater) + m x (333.5 J/gm)
where m is the mass of the water in grams. To calculate the mass of the water, we measure the volume of the tube and use the fact that water has a density of 1 gram per cubic centimeter. The amount of energy output is
K.E. = 1/2 x mboat x v2
where v is the velocity of the boat. Using these two numbers, we get that the efficiency of the motor boat engine is approximately
Efficiency = Q/K.E. x 100%
This is not the actual efficiency since not all of the water in the tube boils. A better estimate might be achieved by only measuring the volume of the heated portion of the tube.
Another result of the Second Law is that heat will always flow spontaneously from hot temperatures to cold. In the South, especially in July and August, we would like to have heat flow from cold to hot. If we could do this, then we could make cool rooms colder, i.e., we could have air conditioning. Can we do this? Well, of course, we can. However, to do it, we must input work to get heat to transfer from cold to hot. In a sense, we must get the engines in the previous experiments to operate in reverse.
For this experiment, we will be using a commercial product, the Pasco Thermoelectric Converter apparatus. This is a device that transfers heat between two metals using electricity. Along with this device, we will need two Styrofoam cups, two thermometers, and a power supply. First, find the mass of the cups, and then add equal amounts of water to each. Place one end of the converter into each cup. Hook the converter up to the d.c. section of the power supply. Place a thermometer in each cup and measure the temperature. Turn the power supply on so that it is outputting 5V and 3A. Take a measure of the temperature of the water every minute until the cold side has experienced a 3 degree temperature drop. Turn the power supply off.