# Heat

There is an easy way to show that hot and cold are subjective terms. That is, what one person calls hot may not necessarily be hot to somebody else. Not only that, you can even be fooled in thinking that one thing is simultaneously hot and cold! To do this, you’ll need three bowls of water. One is at room temperature, the second one is very cold, let’s say it’s been left in the freezer for a good half an hour but hasn’t frozen yet. And the third one has hot water; not so not that it will scald you but hot enough that you would want to take a hot bath in that water. Now, line up the bowls side by side with the hot bowl on the left, the one with room temperature water in the middle and, finally, the cold one on the right. Dip your left index finger in the left hot bowl and at the same time dip your right index finger in the cold bowl. Leave them there for at least thirty seconds. Next, dip both index fingers at the same time in the middle bowl. What do you feel? Is the water in the middle bowl hot or cold? This little and easy to do experiment can clearly show us how unreliable our judgement of temperature can be.

But what is temperature to begin with? And how is it related to heat? Temperature is a measure of how hot or cold something is. From a scale of 0 to 100, if something has a temperature of 80 then it’s hot whereas it’s cold if it has a temperature of 5. That’s typically how we interpret temperature. But without a scale to give a measure of temperature, how could we tell if something is hot or cold? Simply by touching it won’t do or, rather, is not always reliable as we’ve seen in the simple experiment above.

Something feels hot because the difference between its temperature and your temperature is greater than zero. For example, the temperature of water coming out of the hot tap is about 45 degrees Celsius while your hand’s temperature is about 36, giving a difference of 45 minus 36, i.e. 9 degrees. However, the temperature of water from the cold tap is 19 degrees Celsius. This gives a difference of 19 minus 36, i.e. -17 degrees. Because one is negative and the other positive, we interpret it as cold and hot respectively.

What we must take from this is that regardless of what scale we use, whether 10 means cold and 50 hot, it’s the difference in temperature that matters, not the absolute. Hotness and coldness is relative. Something is hot relative to something else. Using our hand to judge whether something is hot or cold is inaccurate and unreliable. We need something more adapted for measuring temperature. We need a thermometer. A thermometer is an instrument which contains a substance that reacts to heat in a certain way. It could be that it changes its volume when its heated or that it changes its electrical conductivity or it could even change its colour. Whatever the property is that changes with heat, this characteristic of the substance can be used to detect changes in temperature and therefore measure how hot or cold something is. Mercury, for instance, expands when heated. For this reason it’s used in a thermometer. As it expands it occupies more volume and because the only available space for it to expand into is the thin tube inside the thermometer, then all it can do is fill in the tube as it rises. As such, if we observe that the mercury level rising in the thermometer, we can deduce that the temperature of the object being measured is getting higher and higher. Conversely, if the mercury level goes down, the temperature of the object is therefore lowering.

We’ve decided, or rather a bunch of scientists have decided, that if the mercury is at a certain level when the thermometer is placed in a container of melting ice, then it’s going to have a value of 0 whereas the level when it’s in boiling water then it’s value shall be 100. This scale is called the Celsius scale and is one which is commonly used. By the scale into one hundred parts, we obtain a more practical scale to measure temperature. We can tell that, by placing the thermometer in our mouth, our body temperature is 37 degrees Celsius because the mercury rises to the 37 mark.

Now if we place the thermometer is some beaker and the mercury level remains at the 37 mark then we can conclude that the content of the beaker has the same temperature as our body. It cannot be of any other temperature. This is a fundamental law in the physics of heat. It’s called the zeroth law of thermodynamics. It tells us that if A and C are at the same temperature and if B and C are also at the same temperature the A and B must have the same temperature. It sounds trivial putting it that way. Mathematically speaking what we’re saying is this: if A = C and if B = C then A = B. It’s simple but it’s the basis of the thermometer. Here, in our example, C is our thermometer and it’s allowing us to deduce that two substances have the same temperature because they both show the same value on the same thermometer.

So much for temperature. What about heat? What does that mean?

Heat is a form of energy. More precisely, it’s a form of energy related to the thermal energy of a system. To understand what thermal energy means we have to go deep into the structure of matter, right down to the molecular level. Matter, as we know, is not just a block of stuff. Rather, it’s composed of smaller parts called molecules. The molecules are bound together by forces and depending on how they are bound, i.e. either very tightly together or loosely moving about in complete chaos, then matter assumes different states (solid, liquid or gas). In the solids, the molecules are tightly packed together, less so in liquids and in gases, the molecules are free to move about at random.

The moving about of molecules is down to two types of movement. One is just like vibrating on the spot and the other is actual translation from one place to another. In solids, the molecules mostly vibrate; they are not so free to move about. In liquids, the molecules can vibrating and can also move from one spot to another, albeit as a group or in layers. They do still keep some bond between them. This is why liquids can flow unlike solid. Gases, however, are the epitome of randomness. The gas molecules are not only vibrating but moving about like crazy.

The vibration of molecules in matter is related to its temperature. That is, what we observer as a high temperature in a substance is in fact a manifestation of how violently the molecules are vibrating in that substance (whether it’s solid, liquid or gas). The more the molecules vibrate, the higher the temperature of the substance. Why do they vibrate in the first place? Well, motion is also a form of energy. By adding energy to the substance, in the form of heat, then this energy is transformed into the energy of motion in the vibrating molecules. (A nicer name for energy of motion is kinetic energy.)  With increasing kinetic energy, the molecules start to vibrate more and more. This is why we register a rise in temperature when we heat something. The heat energy we are supplying to the substance is being converted into kinetic energy of the molecules. Thermal energy is just this: the sum of the kinetic energy of the molecules of the substance.

Now, from our own experience we have noticed that we just can’t keep heating a solid forever. Some sort of reaction would occur. Whether it starts to melt or burn or glow or evaporate, there is a noticeable change in the substance. That is to say, we can’t keep adding heat and increasing the kinetic energy of the molecules without causing some physical or chemical change in the substance. One common physical change we notice is that the solid starts to melt when its hot enough. What then is behind this change of state in matter? What causes it to change from solid to liquid?

The more heat we supply, the more the kinetic energy of the molecules increase. But remember that there is another way in which the molecules move: they can move from one point to another or have a translational motion. So, some of that heat energy also goes into the translational motion or translational kinetic energy. On the one hand, the molecules are vibrating more and more and on the other they are trying to move away from each other. Because there is a force which binds them together, they just can’t fly away by themselves. They are bound together. But by given them enough energy to overcome that force, they can start to break from that bond. This energy which allows them to break the bond is called potential energy. The heat energy is therefore going into the kinetic and potential energy of the molecules. Kinetic energy is responsible for the temperature of the substance while potential energy is responsible for the state it is in. When it changes from solid to liquid, the molecules are able to break that bond and move about more freely: the substance changes state from solid to liquid. We commonly call this melting.