Hotness and Coldness are familiar. A thermometer such as a mercury-in-glass type measures degrees of "hotness" by utilising the property of mercury which, like most things, expands when it gets hotter. As it expands, the column of mercury fills more of the tube, and so we can read off "how hot it is" on the scale. The scale is typically based on the melting point of ice and the boiling point of water. A Fahrenheit scale has the ice point marked 32 and the steam point marked 212 with 180 divisions or degrees. A Celsius or centigrade scale has the ice point at zero and the steam point at 100.
The graduation of the glass tube can obviously be continued above and below these fixed points. If the mercury rises 20 divisions above the 100 point on the Celsius thermometer, then the temperature is 120 degrees Celsius. But this extrapolation is limited in practice because if the temperature falls too low the mercury freezes. Different fluids can be adopted. Ethyl alcohol in glass can be used down to minus 166 degrees F while the electrical resistance of platinum wire can be used up to 1800 degrees.
Here we show again the diagram that was used to help explain the Reversible Carnot Cycle. It shows a reversible engine E driving a reversible heat pump P. The relationship between Q1, Q2 and W depends only on the temperatures of the hot and cold reservoirs, just as Carnot predicted. But temperature must be defined in a more fundamental way. The degrees on the thermometer are only an arbitrary scale. Kelvin took the bold step in 1851 of defining an absolute temperature scale in terms of the efficiency of reversible engines: The ideal "never attainable" efficiency is the ratio of work output to heat input (W/Q1) of the reversible engine E and it equals: Temperature Difference (T1 - T0) divided by the Hot Reservoir Temperature (T1). It is known as the Carnot efficiency, taking its name from Sadi Carnot. The device P can be any refrigeration device we care to invent, and the work of Kelvin tells us that the Minimum Work, W necessary to lift a quantity of heat Q2 from temperature T0 to temperature T1 is:
Q2 multiplied by the ratio Temperature Difference (T1 - T0)/Cold Reservoir Temperature (T0). The temperatures must be measured on an Absolute scale.
Refrigeration "efficiency" is usually defined as the heat extracted divided by the work input.
This is called COP, Coefficient of Performance.
The ideal "never attainable" value of COP is given by:
Kelvin's Glasgow Statue
Absolute Temperature and Absolute Zero
Kelvin's innovation has been universally accepted. His work earned him the honour of a statue in Glasgow and the naming of the unit of absolute temperature. It's called the Kelvin.
The size of the temperature unit. Given any 2 reservoirs, any number can be used to describe the temperature of one of them. Then a measurement on a reversible engine will define the number which must be used for the temperature of the other. The only choice is is the size of the temperature unit. If we fix 100 degrees as the difference between the boiling and freezing points of water, it turns out that this is 373 degrees and 273 degrees on the absolute scale. This is written 373K and 273K. The Kelvin (K) is the unit of absolute temperature.
It is impossible to go below absolute zero. It can be shown that such an action contravenes the second law of thermodynamics, but that is beyond the scope of this page. Its not even possible to reach absolute zero in the absence of a perfect insulator.