Calorimetry - The Study of Heat Transfer

What is Heat?

Heat and temperature are related to each other. However, temperature does not measure heat. Heat is a measure of the total energy of all the particles in a substance. Temperature is a measure of the average energy (kinetic) of particles at a particular location within a substance. Objects that may be "cold" could in fact have a tremendous quantity of heat. An iceberg is a good example of an object with a low temperature (average kinetic energy in one spot) but a large quantity of heat. This is a consequence of the iceberg's very large mass (number of particles). The individual energy of each particle may be small, but collectively they add up to a very large value. This is analagous to a dump truck full of nickels. The individual value of each nickel is small (like the energy value of each iceberg particle), but the overall monetary value of the dump truck is large because it holds so many nickels.

Temperature

There are three common temperature scales in use throughout the world. The first is the Fahrenheit scale. This scale is in common use in the United States, but not much anywhere else in the world. The second scale is named after Anders Celsius. It is based on the freezing and boiling points of water. Although originally 0 was set as the boiling point temperature and 100 as the freezing point, this was reversed by Carl Linnaeus shortly after Celsius's death. The third temperature scale is named after Lord Kelvin, and is frequently referred to as absolute temperature since there are no negative values on this scale. This is a consequence of its basis on absolute zero, a concept introduced by Lord Kelvin.

Absolute Zero

Absolute zero is the temperature at which particles reach a minimum amount of energy, vibration, and motion. The kelvin scale is based on this temperature, and is 0 K. On the Celsius scale, absolute zero is -273.15°C. On the Fahreneheit scale, it is nearly -460°F.

Specific Heat

The specific heat of a substance is the amount of heat needed to change the temperature of 1 gram of a substance by 1 degree Celsius. Notice that this definition says "change" and not "raise" or "lower" the temperature. The same amount of energy is needed to raise the temperature of a substance by 1 degree or lower it by 1 degree. The difference is whether the heat is being added to or removed from the substance. Metals generally have low specific heat values. Consequently, they easily warm up and cool down. Liquid water has one of the highest specific heat values of any substance. Water is very difficult to warm up and cool down. A pot of boiling water on a stove is good evidence for both these statements. The pot will be uncomfortable to touch after a few seconds of heating, while it will be difficult to notice any change in the water's temperature. Once the water inside the pot has been brought to a boil (and the source of heat removed), it will remain lukewarm long after the pot has cooled down.

What is a Calorie?

The calorie is a unit of measurement of heat. It is no longer used, as the SI unit joule is favored. One calorie is the amount of energy needed to change the temperature of 1 gram of liquid water by 1 degree Celsius. Notice the similarity to the aforementioned definition of specific heat. In short, one calorie is the specific heat of water. Since the specific heat of water is also 4.184 J/g°C, the conversion factor for calories to joules is:

1 calorie = 4.184 J

In the United States, the word calorie is most often associated with food. There are some clarifications that need to be made when trying to compare the usage of the word calorie in a discussion of heat and food labels. Firstly, the caloric content of food is not the total energy contained within the particles of food. Rather, it is a measure of the net energy gained when the body breaks down the molecules that make up the food. For this reason, a bottle of water will have zero calories printed on the label. Since the particles of water cannot be digested (broken down chemically by the stomach), there is no energy gained from drinking water. It would be incorrect to state that "water has no energy/zero energy" since the particles of water have mass, and thus have energy.

Some final notes about caloric content of food. The caloric values given on food labels are kilocalories, meaning that a candy bar that has "140 Calories" printed in its label is actually 140 kilocalories, or 140,000 calories. Most doctors recommend a daily diet of 2,000 Calories, and once again this represents kilocalories. Such a diet allows an individual 2,000 kilocalories or 2 million calories. In an effort to keep the numbers small (and likely more manageable), kilocalories are used.

Calculating Heat

q = mCpΔT

The above equation is used to calculate the heat that is gained/lost by a substance. The variable q represents heat, measured in joules. Cp represents specific heat (in J/g°C) and m is the mass of the substance in grams. Lastly, ΔT represents the change in temperature of the substance. The temperature can be degrees Celsius or kelvin, since both scales have the same increments for their scales.

What is the amount of heat needed to raise the temperature of a 54.0 g block of copper from 10.0°C to 65.0°C?

Use the specific heat table to find the correct value for copper. This will be substituted for Cp. ΔT is calculated by subtracting the initial temperature from the final temperature. That is:

ΔT = Tf - Ti = 65.0 - 10.0 = 55.0°C

Finally, substitute the mass into the equation:

q = (54.0)(0.385)(55.0) = 1140 J

This value can be converted to calories by dividing by 4.184 (1 calorie = 4.184 J):

q = 1140/4.184 = 272 cal