Heat Transfer: Understanding Energy Exchange

For thousands of years, people have noticed the effects of heat and cold. Particularly, they noticed that, when they came in contact with an object that was hotter or colder, their bodies seemed to try to reach the temperature of the object. Also, the object seemed to reach the temperature of their bodies. So, they developed an interest in the workings of this phenomenon. Not too long ago, the Fahrenheit, Celsius, and Kelvin scales were developed to quantify the changes in temperature and what this meant for the objects.

In class, we developed the relationship between the Fahrenheit and Celsius scales.

We know that temperature is also a measure of energy. Hence, when something changes temperature, it also changes the amount of energy it has. But, where does this go or how? To illustrate this, first we had to consider how will a bubble filled with methane act. My group said that the bubble would stay at the same altitude, but, as it turns out, air is more dense than methane; hence, the bubble floated upwards due to buoyancy.

Then, we explored what happened when we lighted this bubble on fire. Naturally it burned, but where did the flame go?

As seen the flame traveled and expanded upwards. There are two reasons for this. First, the particles of methane gas continue to travel upwards even while on fire because they already had momentum. And second, the energy flowed along with the particles. Hence, energy and temperature travel through the interaction of molecules.

Next, we explored this a little more and calculated the final temperature of a mixture of waters at different temperatures, one at 25 C and the other at 65 C.

It was predicted that, when the two cups of water mix, their temperatures would approach each other until they become the same. In this case, the final temperature is 45 C, exactly the average, but what happens when the masses of waters are different? For this, we used Fourier's law and the principle of conservation of energy. (The top equation in the picture.)

And we set new values for mass. Then we solved and predicted the way in which temperature would change.

And our results were confirmed.

But now, what happens when there is a barrier between the liquids?

Well, since the hot water molecules are moving a lot faster, they are bouncing lively against the barrier as they share their energy and the barrier warms up or gains energy. Then, the barrier is warmer because the atoms it's made of are vibrating a lot faster and, when a cold water molecule bounces against it, it picks up the energy from the barrier. Nevertheless, the barrier has the effect of slowing the flow of heat.

As shown in the graph, the temperatures eventually become the same and most molecules have the same energy, but it takes a lot longer.

So, what is the effect of a barrier and how can we calculate heat flow through materials?

For this we use the last equation. Here we took into account that heat flow depends on the length of the path that heat takes, the difference in temperatures, the conductivity of the materials, and the area of contact. And, we applied it to every layer as in the following picture with each layer having its own heat calculation.

As shown, Prof. Mason was astonished at the work of his students.

Our derivations confirmed that an object rises in temperature when there is an input of energy. Hence, the an experiment was made to see if an immersion heater delivers as much energy as it pulls. The immersion heater was rated to 297.6 W and run for 20 secs. and pulled 5952 J. The initial temperature of 100 g of water was 24.3 C and the final 27.6 C.
As shown, the relationship between heat and temperature is linear and dependent on the mass of water. When this is factored out, the slope turns out to be the specific heat capacity of water. And the equation was Q/m = c T.
What this means is that heat and temperature are proportional and that either one can be used to measure the other. And, the slope of the line was the specific heat capacity of the substance.