Absolute 5/25/22

Science with Richard Bleil

Early thermodynamicists had no idea what temperature was.  They ascertained that temperature was a measure of something but didn’t really understand what it was.  They invented the term “heat”, a term that has persisted, and defined temperature as a measure of heat quantity.  The higher the temperature, the more heat is present.  Without knowing what heat is, they defined heat as simply that which transfers from regions of high temperature to that of low temperature. 

Today, we understand that heat is a measure of the average kinetic energy of atoms and molecules.  Kinetic energy is the energy of motion, so the higher the temperature (and the higher the quantity of heat), the faster atoms and molecules move.  If we think of billiard balls, as they smash into each other, they transfer their kinetic energy to each other.  Atoms and molecules do the same, so as high temperature matter is in contact with cold, the faster moving higher temperature atoms collide with the slower low temperature atoms, making them move faster, and increasing their temperature. 

Understanding what heat is allows us to better understand the concept of absolute zero.  If higher temperature means faster moving atoms and molecules, then there must be a point where there is no motion at all.  At loser temperatures, atoms and molecules move slower and slower, but the limit must be no motion at all.  This is the hypothetical absolute zero temperature. 

Experimentally, we perform Boyle’s Law experiments.  Boyle’s Law tells us that the lower the temperature of a gas (at constant temperature and amount of gas), the less volume it will occupy.  It’s a simple experiment.  Basically, you take a syringe, which has volume measurements on it, and put it in different temperatures (like room temperature, boiling water, ice water where temperatures can all be measured).  In the end, you plot volume versus temperature and perform what we call an “extrapolation”.

Mathematically, extrapolation can be thought of as extending the line of a set of data points well beyond the limits of the experiment.  As we plot temperature and volume, if we are careful, we see that the relationship between volume and temperature is linear.  That is, all of the experimental points will lie on a straight line.  So, you can take this line and extend it (using, for example, a ruler or a mathematical technique) to the point where the volume is zero.  Volume can never be less than zero, so this volume represents the theoretical limit of this experiment.  If you are very careful, this line will cross the temperature at -273.15 degrees Celsius (many people know absolute zero is -273 degrees Celsius, but few realize that there are more digits, of which I only know two off of the top of my head).  This volume is where all motion would stop.  It is absolute zero. 

It’s important in calculations to use a temperature scale that can never be zero.  Mathematically, dividing a number by zero is undefined, so temperature scales like Celsius cannot be used.  But take the Celsius scale and add to it the value of absolute zero (add 273.15), and you have a new temperature scale (the Kelvin scale) that can never be zero since no temperature below absolute zero is possible, and even absolute zero is only possible theoretically.  In calculations, then, we need to use an absolute scale. 

Of course, if we have an absolute zero in the Celsius scale, there must also be an absolute zero in the Fahrenheit scale.  This is -459.67 degrees Fahrenheit.  In calculations, of course, we cannot use the Fahrenheit scale since it goes through zero, but, again, if we add 459.67 to the Fahrenheit scale, we get a second absolute scale, called “Rankine”. 

One quick addition that I personally find interesting.  Degrees are only used in relative scales like Celsius and Fahrenheit.  These scales are built on something relative, such as the Celsius scale that is set according to the freezing point of water (set to zero) and the boiling point (set to 100).  Thus, it’s all relative to the boiling and freezing point of water.  Thus, if we are in a warm day, where the Celsius temperature is twenty, we would say the temperature is twenty degrees Celsius.  However, absolute scales are independent of any relative fixed point, so we need not use the word “degrees”.  Thus, it is actually inappropriate to say the temperature is (273+20=)293 degrees Kelvin.  Instead, we would simply say the temperature is 293 Kelvin. 

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