What do we mean by the temperature of an object? At first thought, this might seem like a very subjective thing. After all, what might seem like a cold day to you might seem like a wonderfully comfortable day to me.  In our understanding of temperature as a measure of the hotness or coldness of an object or substance (water, air, ...), we run into trouble in defining exactly what temperature means. 

It turns out that we already have the fundamental tools for understanding what temperature means.  It should come as no surprise that a measure of the temperature of an object or system boils down to a discussion of the energy contained in that object or system.  In particular, the temperature of a system can be defined in terms of the microscopic average kinetic energy of the particles (atoms or molecules) that make up the system.  Something that is hot has lots of atoms bouncing around vigorously within the object.  What your finger senses as hot when you touch this object is the sensation of the atoms in that object undergoing energetic collisions with the atoms in your fingertip. Since collisions tend to transfer energy from the more energetic particles to the less energetic particles, it follows that your fingertip picks up energy when you touch something which is hot.  This also explains from a microscopic point of view why heat (the transfer of energy due to a temperature difference) always goes from something hot to something not-so-hot with which it is in contact.

We will discuss the microscopic view of things a bit more in the section on the Ideal Gas.  Until then, we will not be doing anything more  with this microscopic point-of-view.  Nevertheless, we can gain a very simple but fundamental understanding of some thermodynamic processes in terms of this simple microscopic picture.  It also serves to point out that there is indeed a very precise microscopic definition of the temperature of an object. Macroscopically, we tend to define temperature as a relative measurement of some sort of predetermined thermodynamic event (the ice melts; the water vaporizes; the mercury expands until it reaches a given mark; etc.).  This macroscopic relative measure brings us to the topic of temperature scales.

We will be concerned with three temperature scales in this course: the Fahrenheit scale, the Celsius scale, and the Kelvin scale.  Each of these scales is a linear scale, which means that we will define the scales and conversions between these scales in terms of what are effectively slopes of the linear plots relating the various temperatures (even though we won’t bother drawing these plots).

These temperature scales can be defined (for our purposes) in terms of the freezing and boiling points of pure water at sea level.  (It takes two points to define a slope....)  These freezing and boiling points of water are given in the table below for the various temperature scales of interest.  You  should commit these temperatures to memory if you do not already know them! For reference, an average or typical temperature representing room temperature is also given.

Using the fact that these temperature scales are all linear scales, we can simply  convert from a temperature reading in one scale to the corresponding reading in another scale.  If you take a reading in temperature scale 1, T_reading, and  wish to find its corresponding unknown value in temperature scale 2, T_x, then we need only use the known temperature readings in the two scales for the  freezing and boiling points of water to find the unknown temperature reading:

Basically what this equation is saying is that, if we were to make a plot of various temperature readings using the temperature scale 2 on the vertical  axis, and of the corresponding readings using temperature scale 1 on the horizontal axis, then we would get a straight line.  Using any two points on  this line (the unknown point and the freezing point, or the boiling point and the freezing point – or any other two points, for that matter!) we could then  compute the slope of the line. Since it’s a linear relationship, the slope would be the same no matter which two points we used.  That is all the equations  above are saying.  It then gives us an immediate way to compute a temperature in one scale using a reading from another, as the next example demonstrates.