Energy, Work, Heat, Temperature

Energy, Work, Heat, Temperature

I. Energy

Energy is: the ability (or capacity) of a system to do work or supply (or produce) heat.

(1) Kinetic energy is the energy associated with motion; the faster an object moves, the more kinetic energy it has. There is an equation which governs this:

K.E. = (1/2) mv2

m means mass and v is velocity. This equation means that the general units on kinetic energy are:

(mass) (distance)2 (time)-2

Since any mass, time or distance unit could be used, it has been agreed to standardize on specific units for these three quantities and they are the kilogram, second and meter. Inserting them in the above equation gives:

(kg) (m)2 (s)-2

This unit has been given a name: Joule. This is in honor of James Prescott Joule, who in the mid-1800s did pioneering work on energy. The Joule is the standard metric (or SI) unit for all energy.

By the way, an older energy unit is still around. It is called "calorie" and it gets a bit of a mention, but not much.

(2) Potential energy is energy that is stored by virtue of position. There are several different types of storage, of which these four are examples.

(a) Gravitational - this is the most familiar. A rock poised to roll down a hill has potential energy. A ball thrown into the air gains more and more potential energy as it rises. The higher in the gravity field you go, the more potential energy you gain.

(b) Electrical - in certain materials, you can remove electrons from one area and send them to another. The area losing the electrons becomes more and more positive and the area gaining them becomes negative. The greater and greater the charge difference, the more energy is stored within the system. An example of this is a storm cloud about to "hurl" a lightning strike Earthwards.

(c) Chemical - this is slightly more complex. Certain chemicals have bonds which require little energy to break. This energy must be put into the bond to break it. However, during the course of the chemical reaction, new bonds form which give off MORE energy than that which was put in. Commonly, these reactive compounds are said to "store" energy, but the truth is that the energy released came from a process of first putting in and then getting back more than you put in.

The positional aspect comes from first breaking bonds between atoms (which takes energy) and then rearranging the atoms in new positions to form new bonds (which gives off energy).

If you get back more than you put in, this is called exothermic. The net potential energy converted in the reaction shows up as heat, that is the area around the reaction goes up in temperature. If you get back less than you put in, this is called endothermic. The increase in potential energy of the newly made compounds is reflected in a heat flow from the surroundings into the chemicals, resulting in a temperature drop in the surroundings.

(d) Nuclear - the famous equation E = mc2 governs this source of potential energy. We can consider the mass itself to be potential energy, since it can be converted from a form not being used (while it is the mass), to kinetic energy. This type of potential energy is released (in measurable amounts) during radioactive decay, fission and fusion.

II. Work

The usual definition of work is as follows: a force acting over a distance

A more wordy definition is: the transfer of energy from one mechanical system to another. It is always completely convertible to the lifting of a weight.

III. Heat

There is a lot of misunderstanding about what heat is. Heat is not a thing, heat is a process.

Here's the definition: heat is the transfer of energy between two objects due to temperature differences.

Notice that the name of the transfer process is heat. What gets transfered is energy. Heat is NOT a substance although it is very convenient to think of it that way. In fact, it used to be thought that heat was a substance.

There is some circularity to the definitions used:

(a) energy does work or produces heat, but

(b) heat is a transfer of energy.

Ultimately, energy is expressed in the motion of substances. If it is moving, it has energy. If it has the capacity to move, there is some potential energy stored away.

IV. Temperature

Generally speaking, the temperature discussed is absolute temperature, measured in Kelvins.

Here's the definition: temperature is a property which is directly proportional to the kinetic energy of the substance under examination.

By the way, it's OK to use temperature differences measured in degrees Celsius. That's because the "size" of one degree Celsius equals one Kelvin. Also, the term "degrees Kelvin" is NOT used.

Here's another definition: temperature is the property which determines the direction heat will flow when two objects are brought into contact.

Two last points, just by the by:

(1) When two bodies are in thermal equilibrium with a third body, then they must be in thermal equilibrium with each other. This is called the Zeroth Law of Thermodynamics and is the basis for temperature measurements, since the thermometer must come to thermal equilibrium with the object being measured.

(2) An important issue in temperature measurement is the ability to accurately and reproducibly measure temperature. To that end, there are on-going efforts at the international level to set temperature standards and ensure that the scientific world gets good data. A recent issue of discussion concerns how to accurately measure temperatures below 0.1 Kelvin. After all, your ordinary laboratory thermometer just will not do at those very low temperatures.

Specific Heat

Here is the definition of specific heat: the amount of heat necessary to move 1.00 gram of a substance 1.00 °C

Note the two important factors:

1) It's 1.00 gram of a substance

2) and it moves 1.00 °C

Keep in mind the fact that this is a very specific value. It is only for one gram going one degree. The specific heat is an important part of energy calculations since it tells you how much energy is needed to move each gram of the substance one degree.

Every substance has its own specific heat and each phase has its own distinct value. In fact, the specific heat value of a substance changes from degree to degree, but we will ignore that.

The units are usually Joules per gram-degree Celsius (J / g °C). Sometimes the unit J/ kg-K is used. This last unit is technically the most correct unit to use, but since the first one is quite common, you will need to know both.

Here are the specific heat values for water:

Phase J g-1 °C-1 J kg-1 K-1

Gas 2.02 2.02 x 103

Liquid 4.184 4.184 x 103

Solid 2.06 2.06 x 103

Notice that one set of values is simply 1000 times bigger than the other. That's to offset the influence of going from grams to kilograms in the denominator of the unit.

Notice that the change from Celsius to Kelvin does not affect the value. That is because the specific heat is measured on the basis of one degree. In both scales (Celsius and Kelvin) the jump from one degree to the next are the same "distance." Sometimes a student will think that 273 must be involved somewhere. Not in this case.

Specific heat values can be looked up in reference books.

How to Determine the Specific Heat of a Substance

We are going to determine the specific heat of copper metal. Now this has already been done many times, so the value is available in reference books. We will pretend that is not the case.

Obviously, we need some pure copper, so we take a small piece of it. Let's say we use 15.0 grams. The shape does not matter.

We place the copper metal into an open beaker filled with boiling water and allow it to sit. We allow it to sit until all of the copper metal is the same temperature as the boiling water. We know what the temperature is, don't we?

It's 100.00 °C.

Now, how long it sat in the boiling water is immaterial. It sat long enough. If you were doing this experiment for real, you might wind up doing the exact same experiment more than 100 times.

Now comes a real key step. As quickly as possible, we pull the metal out of the boiling water and transfer it into a beaker which holds 100.0 mL of some much cooler water, say 25.00 °C. We know this because we measured the temperature with a thermometer.

The hot copper metal cools down and the water heats up, until they both get to the same ending temperature. We record this with a thermometer and find that it is 25.35 °C. We now know two different Dt values. One is 100.00 minus the ending temperature (the copper) and the other is the ending temperature minus 25.00 (the water).

At this point we will make a key assumption, which will make our task easier. That is to assume that all the heat lost by the copper winds up in the water. In reality this is not the case. In an actual experiment, the heat transfer will not be 100% and you have to take steps to compensate for those losses. We will ignore them.

The paragraph just above, when stated in a thermochemical equation, is:

qcopper = qwater

By substitution, we have (copper values on the left, water values on the right):

(mass) (Dt) (Cp) = (mass) (Dt) (Cp)

Putting the numbers in place gives us:

(15.0 g) (74.65 °C) (x) = (100.0 g) (0.35 °C) (4.184 J g-1 °C-1 )

Solving gives 0.131 J g-1 °C-1

Notice the rather small temperature gain by the water (25.00 to 25.35) and the very large temperature change (100 to 25.35) of the copper. This is typical of problems of this sort.

Notice that 100.0 g of water is used in the calculation above, while farther above the text says 100.0 mL of water. The mass of water present is determined by volume times density. Since the density of water is 1.00 g mL-1, the calculation is:

100.0 mL x 1.00 g mL-1 with the answer being 100.0 g.

The Time-Temperature Graph

We are going to heat a container that has 72.0 grams of ice (no liquid water yet!) in it. To make the illustration simple, please consider that 100% of the heat applied goes into the water. There is no loss of heat into heating the container and no heat is lost to the air.

Let us suppose the ice starts at minus 10.0 °C and that the pressure is always one atmosphere. We will end the example with steam at 120.0 °C.

There are five major steps to discuss in turn before this problem is completely solved. Here they are:

1) the ice rises in temperature from -10.0 to 0.00 °C.

2) the ice melts at 0.00 °C.

3) the liquid water then rises in temperature from zero to 100.0 °C.

4) the liquid water then boils at 100.0 °C.

5) the steam then rises in temperature from 100.0 to 120.0 °C

Each one of these steps will have a calculation associated with it. WARNING: many homework and test questions can be written which use less than the five steps. For example, suppose the water in the problem above started at 10.0 °C. Then, only steps 3, 4, and 5 would be required for solution.

Above is the type of graph which is typically used to show this process over time. The five numbered sections on the graph relate to the five numbered parts of the list just above the graph.

Also, note that numbers 2 and 4 are phases changes: solid to liquid in #2 and liquid to gas in #4.

Here are some symbols that will be used, A LOT!!

1) Dt = the change in temperature from start to finish in degrees Celsius (°C)

2) m = mass of substance in grams

3) Cp = the specific heat. Its unit is Joules per gram-degree Celsius (J / g °C is one way to write the unit; J g-1 °C-1 is another)

4) q = the amount of heat involved, measured in Joules or kilojoules (symbols = J and kJ)

5) mol = moles of substance.

6) DHfus is the symbol for the molar heat of fusion and DHvap is the symbol for the molar heat of vaporization.

We will also require the molar mass of the substance. In this example it is water, so the molar mass is 18.0 g/mol.

By the way, the p means the specific heat is measured at constant pressure

Step One: solid ice rises in temperature

As we apply heat, the ice will rise in temperature until it arrives at its normal melting point of zero Celsius.

Once it arrives at zero, the Dt equals 10.0 °C.

Here is an important point: THE ICE HAS NOT MELTED YET.

At the end of this step we have SOLID ice at zero degrees. It has not melted yet. That's an important point.

Each gram of water requires a constant amount of energy to go up each degree Celsius. This amount of energy is called specific heat and has the symbol Cp.

Step Two: solid ice melts

Now, we continue to add energy and the ice begins to melt.

However, the temperature DOES NOT CHANGE. It remains at zero during the time the ice melts.

Each mole of water will require a constant amount of energy to melt. That amount is named the molar heat of fusion and its symbol is DHfus. The molar heat of fusion is the energy required to melt one mole of a substance at its normal melting point. One mole of solid water, one mole of solid benzene, one mole of solid lead. It does not matter. Each substance has its own value.

During this time, the energy is being used to overcome water molecules' attraction for each other, destroying the three-dimensional structure of the ice.

The unit for this is kJ/mol. Sometimes you see older references that use kcal/mol.