Heat transfer

Imagine that you are holding in your hands a glass of water. We're going to say that the glass of water is at room temperature, so that's about 20 degrees Celsius, and you are at body temperature, which is about 37 degrees Celsius. Now intuitively, you know that after a while, your hand starts to feel kind of cold, right? So what's going on here? In the physical sciences, we say that what's going on here is called a heat transfer. And the idea is that because we have two different things at different temperatures, specifically because our water's at a lower temperature, energy in the form of heat is going to travel from our body to the water, which means that our body is losing energy, and the cup of water here is gaining that energy. So we are becoming cold, and the cup of water is warming up. Now when I was first learning about heat transfer, I didn't quite understand the difference between heat and temperature, so I just want to go ahead and briefly discuss what the difference is. Heat is the amount of energy that's transferred due to a change in temperature. So I'm going to go ahead and write that out here. Remember that whenever you see a gradient, whether it's a gradient of pressure, or concentration, or in this case, a gradient of temperature, it always means that there is some type of potential energy that's stored up. And since the system wants to achieve its lowest energy possible, if there is no opposing force, the gradient wants to disappear, so this is the basis behind heat transfer. Of course, what sets up this gradient is temperature, and temperature is an absolute quantity. Specifically, it's defined as the average kinetic energy of molecules in whatever we are measuring the temperature of. So to summarize, the point I really want to underscore here is that while temperature is an absolute measure of energy, there is really no such thing as an absolute heat content. Heat should always be described as heat transfer, because it is measuring the amount of heat that is either lost or gained. It's also important to emphasize that heat transfer occurs between a system and its surroundings, which I'm going to abbreviate as surr. So to understand this, let's go ahead and revisit our example above. Now, what's really important to determine here is the direction of heat transfer. Now as I talked about before, we can't really attribute an absolute value of heat content to either the system or the surroundings, but what we can say is, what direction does this heat transfer occur in? What's getting hotter, essentially, and what's getting colder? So the way that physical scientists kind of denote heat transfer is with the lowercase letter q. And so in the case of our system, which is our hand which is becoming colder, the way that this would be denoted is with a minus q, because heat energy is being lost from the system. On the other hand, what you would find after a while if you kept holding this glass of water and then set it down on the counter and measure the temperature is that the temperature of the water would have increased. And essentially, what is going on here is that the energy lost from the system is being absorbed by the surrounding. And so in this case, because heat energy is being gained, this would be denoted as plus q. To state this phenomenon more generally, it's fair to say that the heat that is either lost or gained by the system is equal and opposite in magnitude to the heat that's either lost or absorbed by the surroundings.