Temperature

The physical or chemical state of most substances changes when they are heated or cooled. If we want, as we often do, to correlate state with conditions, we need some sort of way to measure the relative "hotness" of the substance.

Temperature is defined as the degree of hotness or coldness of a substance measured on some definite scale.

Hotness (and coldness) result from molecular activity. As molecules take up energy, they start to move faster, and the temperature of the substance increases. Thus we can say that temperature is a measure of the average kinetic energy of the molecules of a substance.

In order to compare the hotness (temperature) of two substances, we need to define a scale of relative temperatures. This is done by assigning values to two points and dividing up the interval between the fixed points into smaller intervals called "degrees".

Temperature Scales

The two most common temperature scales are the Fahrenheit scale and the Celsius scale. Both are examples of relative Temperature scales.

Gabriel Daniel Fahrenheit (1686-1736), a German physicist, fixed one point using a mixture of salt, water, and ice (0 degrees F) and the other using body temperature (96 degrees F) -- chosen because it is divisible by 2, 3, 4, 6, 8). On this scale, water freezes at 32 degrees F and boils at 212 degrees F.

Anders Celsius (1701-1744), a Swedish astronomer fixed the freezing point of water (0 degrees C) and the boiling point of water (100 degrees C). Because it has 100 degrees, this scale has also been called the centigrade scale.

The Celsius scale is more commonly used in scientific applications in the US, as well as in the rest of the world.

To convert between the scales, first you need to look at the size of the degrees:

Equation 1
and then you need to remember that they don't start at the same place
Equation 2
So to convert from one to the other you use a calculation like
Equation 3

EXAMPLE: What is the temperature in Fahrenheit when it is 70 degrees C?
Equation 4

Absolute Temperature Scales

We've said that temperature is based on molecular motion. Theoretically, there is a condition of no molecular motion (so cold that the molecules stop moving, or zero kinetic energy in the molecules). This point is called absolute zero, and is the lowest conceivable temperature.

Equation 5

As thermodynamics developed, it became useful to define temperature scales which began at absolute zero (so you didn't have to mess with negative temperatures). These scales are called absolute Temperature scales. Two scales are commonly used, set up so that the degree intervals are the same size as the common relative scales.

The Kelvin scale has the same size degree as the Celsius scale. Thus,

Equation 6
The Rankine scale has the same size degree as the Fahrenheit scale, so:
Equation 7
Often, we round the endpoints off to 273 and 460.

Since the degrees are the same "thickness" between Celsius and Kelvin (or between Fahrenheit and Rankine) we need only make an "additive" conversion to adjust between the two.


EXAMPLE:What is the freezing point of water on the absolute temperature scales?
Equation 8

On the other hand, if we want to convert from Kelvin to Rankine, both start at absolute zero, and we only need to use the "multiplicative" conversion to switch (1.8 R/K).

Temperature Intervals

It is important to keep straight that "degree" has a double meaning. It means both a temperature "96 degrees Fahrenheit" and an interval "96 Fahrenheit degrees". In practice, this means that when converting an interval, you don't need to compensate for the zero shift.


EXAMPLE: You have a mixture at 50 degrees F and increase its temperature by 30 C degrees. What is the final temperature?

Equation 9
Don't make the mistake of thinking this is the same as:
Equation 10

References:

  1. R. M. Felder & R. W. Rousseau, Elementary Principles of Chemical Processes (2nd Ed.), John Wiley, 1986. pp. 63-67.
  2. F. W. Kirk & N. R. Rimboi, Instrumentation (3rd Ed.), American Technical Publishers, 1975, pp. 17, 19-21.
  3. Sonntag, R.E., C. Borgnakke, and G.J. VanWylen, Fundamentals of Thermodynamics (6th Ed.), John Wiley, 2003, pp. 32-33.

R.M. Price
Original: 6/3/94
Modified: 11/8/94, 6/21/96, 9/8/98; 5/13/2003

Copyright 1998, 2003 by R.M. Price -- All Rights Reserved

Validated