Certain trace elements are known to be toxic to humans but at the same time are essential for health For example, would you knowingly drink a glass of water containing 50 ppb of arsenic?

The human body normally contains 40 to 300 ppb. Wines contain 5 to 116 ppb of arsenic.

Marine fish contain 2000 to 8000 ppb. Should you stop eating fish? Another compound essential to humans and animals is selenium. We know that 0.1 to 0.3 ppm of selenium is essential to the diet, but that 5 to 10 ppm is a toxic dose. The Delaney Clause of the food additives section of the Food, Drug, and Cosmetic Act has been interpreted as prohibiting the presence in food of any added carcinogen. Can selenium be added to your diet via vitamin pills? What about arsenic?

2.10. Temperature

You can hardly go through a single day without noticing or hearing what the temperature is. Believe it or not, considerable controversy exists among some scientists as to what the correct definition of temperature is (consult some of the references at the end of this chapter for further information). Some scientists prefer to say that temperature is a measure of the energy (mostly kinetic) of the molecules in a system. Other scientists prefer to say that temperature is a property of the state of thermal

equilibrium of the system with respect to other systems because temperature tells us about the capability of a system to transfer energy (as heat).

In this book we use four classes of temperature measures, two based on a relative scale, degrees

Fahrenheit (°F) and Celsius (°C), and two based on an absolute scale, degrees Rankine (°R) and

kelvin (K). Relative scales are the ones you hear the TV or radio announcer give and are based on a specified reference temperature (32°F or 0°C) that occurs in an ice-water mixture (the freezing point of water).

Absolute temperature scales have their zero point at the lowest possible temperature that we believe can exist. As you may know, this lowest temperature is related both to the ideal gas laws and to the laws of thermodynamics. The absolute scale that is based on degree units the size of those in the Celsius scale is called the kelvin scale (in honor of Lord Kelvin, 1824–1907); the absolute scale that corresponds to the Fahrenheit degree units is called the Rankine scale (in honor of W. J. M. Rankine, 1820–1872, a Scottish engineer). Figure 2.2 illustrates the relationships between relative temperature and absolute temperature. We shall usually round off absolute zero on the Rankine scale of –459.67°F to –460°F; similarly, –273.15°C frequently will be rounded off to –273°C. Remember that 0°C and its equivalents are known as standard conditions of temperature.

Figure 2.2. Temperature scales

Now we turn to a topic that causes endless difficulty in temperature conversion because of confusing semantics and notation. To start, you should recognize that the unit degree (i.e., the unit temperature difference or division) on the kelvin-Celsius scale is not the same size as that on the Rankine-

Fahrenheit scale. If we let Δ°F represent the unit temperature difference on the Fahrenheit scale and Δ°R be the unit temperature difference on the Rankine scale, and Δ°C and Δ K be the analogous units in the other two scales, you probably are aware that

Δ°F = Δ°R Δ°C = Δ K

Also, because of the temperature difference between boiling water and ice (Celsius: 100°C – 0°C = 100°C; Fahrenheit: 212°F – 32°F = 180°F), the following relationships hold:

Δ°C = 1.8000 Δ°F and Δ K = 1.8000 Δ°F

If you keep in mind that the unit degree Δ°C = Δ K is larger than the unit degree Δ°F = Δ°R, you can avoid much confusion.

Now to the final point. When we cite the temperature of a substance, we are stating the cumulative number of units of the temperature scale that occur (an enumeration of ΔTs) measured from the reference point (i.e., absolute zero for K and °R, and the freezing point of water for °C and °F). Reexamine Figure 2.2.

Unfortunately, the symbols Δ°C, Δ°F, Δ K, and Δ°R are not in standard usage; the Δ symbol is

normally omitted. A few books try to maintain the difference between degrees of temperature (°C, °F, etc.) and the unit degree by assigning to the unit degree a symbol such as C°, F°, and so on. But most journals and texts use the same symbol for the two different quantities, one the unit temperature

difference and the other the temperature itself. Consequently, the proper meaning of the symbols °C, °F, K, and °R as either the temperature or the unit temperature difference must be interpreted from their usage. What this statement means is to use some common sense.

The following relationships can be used to convert from °F to °R, from °C to K, from °C to °F, and from °F to °C, respectively:

Equations (2.8) and (2.9) are based on the fact that both 32°F and 0°C correspond to the freezing point of water and that Δ°C = 1.8Δ°F.

Suppose you have the relation

T_°F = a + bT_°C

What are the units of a and b? Certainly from what you have learned so far, the units of a must be °F for consistency. Are the units of b equal to the units in the ratio T_°F/T_°C? No, because the reference points for °C and °F differ; T_°F/T_°C is not a valid conversion factor. The correct units for the

conversion factor are Δ°F/Δ°C, a factor that converts the size of a division on each of the respective temperature scales:

Consequently, unfortunately, the units for b are usually ignored; just the value of b is given.

When you reach Chapter 9, you will note that the heat capacity in the SI system has the units of J/(g mol)(K). Does the K in the heat capacity designate the temperature in degrees K or the unit interval Δ K? Now look at some temperature conversion examples.

Example 2.21. Temperature Conversion Convert 100°C to (a) K, (b) °F, and (c) °R. Solution

a.

b.

c.

or

Example 2.22. Temperature Conversion

The heat capacity of sulfuric acid in a handbook has the units J/[(g mol)(°C)] and is given by the relation

heat capacity = 139.1 + 1.56 × 10–1T

where T is expressed in degrees Celsius. Modify the formula so that the resulting expression yields the heat capacity with the associated units of Btu/[(lb mol) (°R)] with T in degrees Rankine.

Solution

The symbol °C in the denominator of the heat capacity stands for the unit temperature difference, Δ°C, not the temperature, whereas the units of T in the equation are in °C. First you have to substitute the proper equation in the formula to convert T in °C to T in °R, and then multiply by conversion factors to convert the units in the right-hand side of the equation to Btu/(lb mol) (°R) as requested.

Note the suppression of the Δ symbol in the original units of the heat capacity and in the conversion between Δ°C and Δ°R.

Self-Assessment Test

Questions