 Constant volume gas themometer (schematic) |
| The definition of a temperature scale is a somewhat tedious operation, the details of which are not required for IB Physics. A brief description of several main points is presented here as background information. |
Temperature is most easily defined in terms of a physical property. The resistance of a wire, the pressure of an enclosed mass of gas, the volume of an enclosed mass of liquid, (mercury, alcohol etc.), in a glass vessel etc.
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Constant volume gas themometer (schematic) |
Two fixed points are selected - for instance the lower value can be defined in terms of the melting point of ice at STP, or the triple point of water*. The upper value can be defined as the boiling point of water again at STP [see the pressure-temperature diagram at right]. The two fixed points are given values on a scale. The Celsius scale has the melting point of ice at zero degrees and the boiling point of water at 100 degrees. The Fahrenheit scale has the somewhat unexpected values of 32°F and 212°F respectively for the same points. The story goes that Fahrenheit used the lowest temperature he could reach with an ice brine bath as zero and his wife's body temperature that he set at 96°F,
So far no problem.
The difficulty arises when an intermediate temperature is measured with say, a resistance thermometer, and a mercury in glass thermometer. The two instruments do not read the same value. The selected properties change in slightly different ways.
The derivation of the ideal gas equation...
... identifies the absolute temperature in Kelvins as the average kinetic energy of the gas molecules in random motion. The properties of a real gas approach those of an ideal gas at low pressures. If a mass of gas is enclosed in a fixed volume (independent of temperature) the pressure is then proportional to the absolute temperature of the gas at equilibrium. Measurements from actual constant volume gas thermometers can be extrapolated to low pressures to more closely approach the ideal gas constant volume thermometer.
The interested student could have a try at designing a constant volume thermometer using a mercury manometer to measure pressure and then look up designs that were of historical importance in developing the concept of temperature.
| Note: the temperature of a gas is defined as the average kinetic energy at equilibrium for a Maxwell-Boltzman velocity distribution only. When temperature is quoted for the solar wind and other situations where the velocity distribution is different the quoted temperature is at best an approximation. |
The triple point of water can be reached by placing a small volume of water in a polystyrene container in a bell jar and pumping out air and water vapor with a rotary vacuum pump. Evaporative cooling reduces the water temperature until ice, liquid water and water vapor coexist in the bell jar at the same time. The unique temperature at which this happens is the triple point (of water).
The demonstration never fails to make Jon Eales very happy. The bell jar at right is being pumped down. A teaspoon full of water at room temperature in a hollow in the polystyrene block boils as the pressure is lowered. Evaporation cools the water until it freezes. Ice and polystyrene are both white - the ice is difficult to photograph but in this case an ice pillar has formed: just visible at right, and shown below from the side.
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Ice pillar actual size. |
