MHS Chemistry
Heat and Energy

Kinetic and Potential Energy
You should recall from earlier science courses that two forms of energy are kinetic energy and potential energy. Kinetic energy (KE) is the energy an object possesses because it is in motion. Moving cars, falling bricks, and vibrating molecules all have kinetic energy. Be careful: it is not energy in motion, or energy going from one place to another, it is the energy something has just because it is in motion.

An object can also have potential energy (PE), which is "stored energy" or "the energy of position." One kind of potential energy is chemical energy, which can be released by breaking bonds: an example of this is a fire releasing the potential energy in a piece of wood. Another kind is the energy an object has because of its position relative to some other object. In physics we usually first learn this as the energy something has because it is high up, that can be released by falling. This actually can be any separation, such as a static-filled balloon and some long dry hair: they are attracted to each other across a small distance in any direction. Also, stretching or compressing a spring can store energy.

So, why are we talking about energy this way? Well, atoms and molecules both possess energy in these forms. They can vibrate and spin and shake in place (KE), or move around from place to place (also KE), they can move close together or far apart (PE), and they might form chemical bonds with each other (also PE). Their energies and changes in energies tell us about them, and what's happening with them.

Temperature & Temperature Scales
We can't really easily know the total kinetic and potential energy in a substance, but we can measure the temperature, which is the average kinetic energy of all the particles that make up a substance. We don't have to use any complicated tools to find this, just sticking a thermometer into a substance will register the amount of KE as a high or a low temperature.

The temperature scale we are most familiar with in America is the fahrenheit scale. The basis of this scale was that 0 F was the lowest temperature obtainable in the laboratory (hundreds of years before refrigerators), by mixing snow alcohol, and ammonium chloride. The 100 degree mark was based on Mr. Fahrenheit's wife's body temperature. This was a particularly poor choice because the basis of a scale should be reproducible in any laboratory in the world with the proper equipment; but in this case one of the pieces of equipment may not have wished to travel, and eventually died. Also, human body temperature varies from person to person, and over the course of the day, and over the course of a month for women. [This is a good story, but I don't remember where I heard it, and it may not be true. Check this out, then this, then this, and this, and this.]

The Age of Enlightenment brought the "System Internacionale" (essentially the metric system), and a more rational basis for many measurement scales. The celsius (or centigrade) scale was based on two more easily reproduced temperatures: The freezing temperature of pure water (0 C at sea level) and the boiling point of pure water (100 C at sea level).

Using F for fahrenheit temperature, and C for celsius temperature, the relationship between these two scales is
F = 1.8C + 32

[What temperature is the same in both scales?][Which scale gives more precise readings, and why?]

Well, naturally, there is a problem with these scales too: if temperature is a measure of the average kinetic energy of the particles in a substance, then does 0 degrees mean there is no motion at all? How can there be two different 0 degrees (0 F is well below the freezing point of water, which is 0 C)? And does a negative temperature imply "un-"motion? Remember that we are mostly measuring vibration of molecules. The problem is that these two scales give convenient numbers for "comfortable" temperatures, but they do not very well correspond with the energy being measured. So the Kelvin Scale was developed to measure absolute temperature. In this scale, 0 degrees represents the temperature at which all motion would stop (there are physical reasons this is impossible). The degrees are the same size in the Kelvin and the Celsius scales, so a 10 degree increase is the same in whether its Kelvin or Celsius. The relationship between the Kelvin and Celsius scales is K = C + 273.15 although in our laboratory we will be fine using 273 instead of 273.15.

[What is 0 K in the celsius scale?][What is 0 K in the fahrenheit scale?][What is body temperature in C and in K?]

Energy Transfer
An easy and convenient way to measure energy changes in chemistry is the technique of calorimetry. This usually means carrying out a reaction in water, and measuring the energy changes of the water. Since the energy change of the water comes from the energy change of the reaction, we can determine energies of reactions and other chemical or physical changes. In order to do this, we must know the specific heat capacity of water, which is the amount of energy needed to raise the temperature of 1 gram of liquid water through a 1 C temperature change. This value is 1 calorie (its the definition of a calorie!) or 4.18 Joules. This quantity is also sometimes known as the specific heat or heat capacity of water. The abbreviation is Cp (because it's measured at constant pressure)
Cp(water) = 1 cal = 1 cal = 4.18 J = 4.18 J
gK gC gC gK

Since a celsius degree and a Kelvin degree are the same size, it doesn't matter if you use K or C for calculations that use this number. Raising 1 gram of water 1 K takes 1 cal; raising 2 g of water 1 C takes 2 cal; raising 2 g of water 2 K requires 4 cal.

The general relationship between a temperature change and an energy change is written as q = mDTCp where q means "quantity of heat change," m is the mass of the substance changing temperature, DT is the change in temperature (always ending T - starting T), and Cp is the specific heat of the substance changing temperature. The specific heat for water is given in the paragraph above, and specific heats for the elements are usually listed on periodic tables. They can be looked up quite easily.

Another way calorimetry can be applied is by putting hot and cold objects together and measuring the changes that take place. We can assume ("pretend") that all the energy moving around stays in the calorimeter, so that the energy change of the hot thing is exactly equal to (and opposite) the energy change of the cold thing. We write this as

q(cold) = -q(hot)
which is the same as  
mDTCp(cold) = -mDTCp(hot)

The negative sign covers the "and opposite" part of the description. This is often used to identify an unknown solid by identifying it's specific heat. A known mass of the solid at a known hot temperature (found by hanging it in boiling water) is added to a known mass of water at a known cold temperature. Once the mixture temperature is found, the only unknown is the specific heat capacity of the unknown.

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