# 1.5: Examples of Models

##### Video: Example of Thermal Interaction

##### Example: Boiling a Pot of Water

Let us consider the physical situation of a pot of water left on an unattended kitchen stove top. We might wish to estimate how long it would take for the 1.0 liter (1.0 kg) of water in the pan to boil away and heat the pan to dangerously high temperatures, perhaps igniting the plastic handle. Let’s also suppose we have previously determined the rate at which energy is transferred from the stove burner to the pan by doing a simple experiment to see how long it takes to heat the 1 kg of water in the pan 10˚C, giving a calculated power input to the water of 1.0 kW.

In this example we are both heating the water and changing its phase; thus we know we will need to include both the thermal and bond systems of the water. How about the pan’s energy systems? If the mass of the water (1.0 kg) is several times larger than the mass of the pan (typically the case), the heat capacity of the pan will be considerably less than the water, since the mass-specific heat of the water is so much greater than steel or aluminum. What about transfer of energy to the environment from the pan? This is tougher to estimate. We do know from experience that water does boil when left on the burner for awhile. So the transfer to the environment is definitely less than from the stove to the pan. We can initially leave this out of the model and consider whether to put it in when we have made the time calculation. What about the stove energy systems? Since we know there is a heat input to the pan of 1.0 kW, it makes sense here to model the water as an open system with the heat input from “the outside.”

So at this point, our energy-system diagram would look like this:

Since the heat input is 1 kW or 1 kJ/s, it would take about 2600 sec or 43 min to boil away the water.

Now we need to examine the reasonableness of our numerical predictions. First, notice that the calculated change in energy of the bond system is about seven times greater than the change in energy of the thermal system. This is at least consistent with the values of heat capacities and heats of vaporization listed in the data table. (We will develop a much deeper understanding of this difference when we further develop our particle model of matter in Chapter 3.) This difference in heats also implies that the water would come to boiling much quicker than it would take to boil it away (something like 5 minutes compared to 38 minutes). Does this correspond to your personal experience when cooking? If you haven’t noticed this considerable difference in times to heat water to boiling and to boil it away, check it out. Earlier, we raised the question weather the pan had an effect on the system. If we included the pan, what energy-system would we need to add? How would this affect our prediction of the time to boil away all of the water?