Energy Measurements

We have learned that chemistry is concerned with the properties of matter and with the energy changes that matter undergoes. We have discussed properties related to the mass and volume of a sample of matter. In this section we examine properties related to energy. Energy is measured either in joules (J) or in calories (cal), where the conversion factor relating the two units is:

4.184 J = 1 cal

The terms kilojoule (kJ), 1000 J, and kilocalorie (kcal), 1000 cal, are also commonly used. The large calorie (Calorie) used in nutrition is equal to one kilocalorie.

The amount of heat energy associated with a particular sample is dependent on its temperature, its mass, and its composition. Let us consider temperature before discussing its relationship to the energy of a sample.

A. Temperature
Temperature measures how hot or cold a sample is relative to something else, usually an arbitrary standard.

1. Temperature scales
Temperature is measured with a thermometer and is most commonly reported using one of three different scales: Fahrenheit (F), Celsius (C) (sometimes called centigrade), and Kelvin (sometimes called absolute).

The relationship between temperatures on these three scales is straightforward if you understand how a thermometer is constructed and calibrated. Two essential features of a thermometer are: (1) it contains a substance that expands when heated and contracts when cooled, and (2) it has some means to measure the expansion and contraction. In the thermometer with which you may be most familiar, the substance that expands and contracts is mercury. In order to measure its expansion or contraction, the mercury is confined within a small, thin-walled glass bulb connected to a very narrow or capillary tube. When the temperature increases, the mercury expands and its level in the capillary tube rises. This increase in height is proportional to the increase in temperature.

A thermometer is calibrated in the following manner. First, the mercury bulb of a new thermometer is immersed in a mixture of ice and water. When the height of the mercury in the column remains constant, a mark is made. This mark is one reference point. The ice-water mixture is then heated to boiling and kept at that temperature while the height of the mercury in the column rises to a new constant level. Another mark is made on the column at this level; this mark is a second reference point.

Further steps depend on whether this thermometer will measure temperature on the Celsius, Fahrenheit, or Kelvin scale. If the Celsius scale is to be used, the reference point for the ice-water mixture is labeled 0°C and that for boiling water is labeled 100°C. The distance between these two reference points is divided into 100 equal segments. If the thermometer is to measure temperature on the Fahrenheit scale, the reference point for the ice-water mixture is labeled 32°F and that for boiling water is labeled 212°F. The distance between these two points is divided into 180 equal segments. If the thermometer is to measure temperature on the Kelvin scale, the ice-water reference point is labeled 273.15 K, the boiling-water reference point is labeled 373.15 K, and the distance between these two marks is divided equally into 100 segments. Notice that K does not use a degree symbol. The symbol K means "degrees Kelvin." As you can see, the temperatures measured by any of these thermometers do not differ; the difference is in the units with which each temperature is reported. The relationships between the three temperature scales are illustrated in Figure 2.7.

FIGURE 2.7 Fahrenheit, Celsius, and Kelvin thermometers.

2. Conversions between the temperature scales
A temperature reading on any one of the three scales can be converted to a reading on any other. First, consider a conversion from degrees Celsius to degrees Fahrenheit. Figure 2.7 shows that, between the temperature readings of the ice-water and boiling-water marks, there are 180 Fahrenheit degrees but only 100 Celsius degrees. This relationship can be written as a conversion factor:

This equation can be rearranged to give the Fahrenheit to Celsius conversion equation:

What is the relationship between the Celsius and Kelvin scales? Because each scale has exactly 100 divisions, or degrees, between the ice-water temperature and the boiling-water temperature, the temperature change represented by a Celsius degree is the same as that represented by a Kelvin. The scales differ in the readings at the ice-water reference point; the reading is 0° on the Celsius scale and 273.15 on the Kelvin scale. Therefore, to convert a Celsius temperature to a Kelvin temperature, simply add 273.15.

Remember that K is not preceded by the degree symbol (°). The symbols for Fahrenheit and Celsius do require the degree symbol; for example we write 212°F and 100°C, but 373.15 K.

3. Melting points and boiling points
Among the data used to identify a substance are the temperatures at which it changes state. The melting point, (mp) of a substance is the temperature at which it changes from a solid to a liquid (or from a liquid to a solid, in which case it may be called the freezing point). The boiling point (bp) of a substance is the temperature at which under normal conditions the substance changes from a liquid to a gas. The melting points and boiling points of several substances are shown in Table 2.9.

The far right column in Table 2.9 shows the physical state of several substances under normal conditions. The physical state is predictable from the melting and boiling points of a substance. A substance that boils below room temperature, 20°C, will be a gas under normal conditions, one that melts below room temperature and boils above it will be a liquid, and one that melts above room temperature will be a solid.

B. Specific Heat
When energy in the form of heat is added to a sample, the resulting temperature change depends on the sample's mass and composition. We are aware of this dependence on composition when we notice that a piece of iron left in bright sunshine quickly becomes too hot to touch, whereas a sample of water with the same mass left in the same location for the same length of time becomes only pleasantly warm. The difference is due to the difference in composition and is expressed quantitatively in the specific heats of the two materials. The specific heat, of a substance is the amount of energy required to raise the temperature of a 1-g sample by 1 degree Celsius. Typically specific heat has units of joules per gram °C (J/g°C).

The specific heat of iron is 0.4525 J/g°C; that is, 0.4525 J is required to raise the temperature of 1 g iron by 1°C. The specific heat of water is 4.184 J/g°C, so 4.184 J are required to raise the temperature of 1 g water by 1°C. Each kind of matter has a unique specific heat. Several are listed in Table 2.10.

Specific heat is a conversion factor that relates energy input to sample mass, composition, and temperature change.

The specific heat of a substance can be calculated if we know the amount of energy required to cause a measured temperature change in a sample of known mass.