Heat and Temperature

It is often said that heat is a form of energy. A more precise statement would be that heat is a process in which energy is added to a system. In particular, a system is heated when energy is added to it as a result of a temperature difference. In this experiment, the source of heat will be the flame of a bunsen burner. The system will be a quantity of water, or some other substance. The substance will be heated because the temperature of the flame is higher than that of the substance.

The energy of a system can take many forms. In mechanics we study kinetic energy (e.g. the energy of water flowing in a river), and potential energy due to a force that acts on the system (e.g. the potential energy change when water flows over a waterfall). Another important form of energy is the energy associated with the molecules that make up the substance -- their kinetic energy of motion and the potential energy associated with inter-molecular forces. We cannot "see" this internal energy directly. But temperature is one measure of how much internal energy a system possesses.

One of the great accomplishments of nineteenth century science was to recognize

To begin the experiment, the instructor will explain how to start your bunsen burner. The air and gas valves have to be adjusted so that you have a compact blue flame. Be sure the instructor checks your burner before you start the experiment. We will be making the assumption that heat flows from the flame to your system at a constant rate. For this assumption to be valid, the size and shape of the flame should not be changed, and the position of the burner under the stand should not be changed, during the experiment.

Temperature will be measured by a thermometer that reads up to above 100 degrees Celsius..

Safety Precaution: Be sure to use the insulated gloves when handling any heated objects.

1. Heat and Temperature Change

Start with about 300 ml of water in a 600 ml beaker. We will want to know the mass of the water, so first measure the mass of the empty beaker on the digital balance; then measure the mass of the beaker with water. Place a screen on the platform and the beaker on the screen. Start the clock to record the time. You don't have to turn the clock on and off. Just keep it going and record the time when you take a temperature reading. Place the burner under the center of the beaker. Record temperature (call it T) and time (call it t) about every minute. (Before recording the temperature, stir the water gently.) Follow the temperature change from room temperature (about 20 or 22 degrees Celsius) up to about 70o C. Then remove the beaker. (Turn off the burner by turning off the gas valve, but don't change the position of the burner or its controls.).

It will be convenient to make a third column giving the elapsed time (call it dt) after the first reading.

Later we will plot a graph with elapsed time, dt, on the vertical axis and temperature on the horizontal axis. Since heat enters the system at a constant rate, the vertical axis will represent the total heat that has entered the water at each reading.

2. Heat and Mass

Now repeat the experiment for 200 ml and 400 ml of water. These quantities don't have to be exact, because, by weighing the water (as before), you will measure the mass precisely. We will want to determine whether the amount of heat needed to increase the temperature of water a given amount is proportional to the mass of water.

3. Another Substance: Glycerine

We will do just one experiment, using about 300 ml of glycerine instead of water. We will compare the heat needed to raise the temperature of 1 gram of water with the heat needed to raise the temperature of 1 gram of glycerine.

4. Analysis

Prepare a graph with dt on the vertical axis and temperature on the horizontal axis. Choose the scales so that data for all three water experiments can be plotted on this one graph. First plot the points for the experiment with 300 ml of water. Use a ruler to draw the best straight line fit to the data. To the extent that the points are close to a straight line, this tells us that the amount of heat, Q, needed to change the temperature by an amount, DT, is proportional to DT. In symbols,

Q ~ DT,
(1)

where the symbol, ~, means "is proportional to".

Use the straight line (not the individual points), to find the time to raise the water temperature by 40o C.

Now plot the points for the 200 ml and 400 ml experiments. Use some method to make sure you can distinguish the points from the three different experiments. Again draw straight line fits to your data, and find the time to raise the temperature by 40o C.

Prepare a table showing the mass of water in the three experiments, and for each the time needed to raise the temperature by 40o C. Plot a separate graph of the data in this table, with elapsed time on the vertical axis and mass on the horizontal axis. Fit a straight line to these three points.

To the extent that this graph is linear, it shows that the heat needed to raise the temperature of water is proportional to mass. In symbols,

Q ~ m.
(2)

Equations (1) and (2) can be combined by writing,

Q ~ mDT.
(3)

Alternately, one can write this as an equation,

Q = cmDT,
(4)

where "c" is a constant. To say c is constant means that Eq. (4) determines the required heat for any mass, m, and temperature change, DT, in an experiment with water, since that's the only substance we have analyzed so far. With another substance, we expect a similar relation, but with a different constant, say, c'.

To compare the water data to the glycerine data, go back to the table that lists the times for DT = 40o C., and add a third column, the time it would take to heat 1 gram of water by 40o. Your three numbers should be about the same, but to get the best estimate, average the three.

Now plot time vs. temperature for the glycerine data. (If it can be done clearly, do it on the same graph as the water data. Otherwise, use a separate graph.) Draw the best straight line fit to the data, and find the time for DT = 40o C. Add this to your table with the water data, and also calculate the time for heating 1 g of glycerine by DT = 40o C. How does this number compare to the number for 1 g of water? Calculate the ratio, using the average you found for water:

[time for 1 g and 40o(glycerine)]/[time for 1 g and 40o(water)]

If this number is, say, 0.55, it means that it takes 55% as much heat to raise the temperature of glycerine a given amount, as it does to raise the temperature of the same mass of water by the same same amount. This ratio is also equal to c'/c (the constant for glycerine divided by the constant for water). The accepted value of this ratio is 0.6.

The discussion above avoids the question of defining a unit of heat. One way a heat unit is defined is as follows: One calorie is the heat needed to raise the temperature of one gram water by one degree. Given this definition, from Eq.(4) you can see that when DT = 1, and m = 1, Q also = 1, so that c for water must be equal to 1. Therefore c', which is called the specific heat of glycerine, will be 0.6. Your ratio, comparing heating times for glycerine and water, gives your value of the specific heat of glycerine.

It is worth noting that the specific heats of most substances are considerably less than 1. In other words, water is unusual in this respect. The large constant for water is responsible for the fact that hot soup cools off more slowly than other hot food. It is also responsible for the fact that weather (temperature variations) is usually more moderate in places near large bodies of water.

Question: What flaws do you see in the assumption that the heat added to the water (or glycerine) is proportional to the time that the burner is on?