Читать книгу Fundamentals of Heat Engines - Jamil Ghojel - Страница 62

Temperature is a fundamental concept, not expressible in terms of other units or physical properties of the devices used to measure temperature, such as alcohol or mercury in glass thermometers or the electromotive force generated in a thermocouple. Physicists have established that temperature measures the kinetic energy of molecules, and the higher the molecular agitation, the higher the temperature and vice versa. The physicist William Thomson (Lord Kelvin) is credited with the establishment in 1848 of the absolute temperature scale (hence the symbol K for temperature) on the basis of Carnot's reversible cycle.

To show how it is possible to arrive at an absolute scale, a hypothetical experiment can be conducted to show that an absolute zero of temperature must exist, and then extend this line of reasoning to develop an ‘energy’ or ‘thermodynamic’ temperature scale.

It was shown earlier that the efficiency of the Carnot cycle is written as

This equation shows that T_L can never be zero or less than zero, for if T_L were equal to zero, the thermal efficiency of the heat engine would be 1, or 100%, which would be a violation of the second law. Also, if T_L were less than zero, the thermal efficiency would be greater than 100%, which would mean a reversal of the direction of Q_L, and heat would be drawn from the low‐temperature source. This also would be a violation of the second law. So, theoretically, the absolute zero of temperature could never be reached.

If a Carnot engine is operated between a high‐temperature source at the temperature of boiling water T_H and a low‐temperature sink at the temperature of melting ice T_L, and the amount of heat received Q_steam and rejected Q_ice were measurable accurately, the ratio Q_steam/Q_ice would be equal to 1.3662. Since Q_steam/Q_ice = T_steam/T_ice,

(1.90)

If the temperature range T_steam − T_ice is arbitrarily divided into 100 equal divisions (call it 100 °C), a second equation can be obtained

(1.91)

The simultaneous solution of Eqs. (1.90) and (1.91) yields the temperature of boiling water and melting ice on a thermodynamic scale:

If the temperature range T_steam − T_ice is divided into 180 equal divisions (call it degrees Fahrenheit, F), we get

(1.92)

The determination of a thermodynamic scale using reversible Carnot engine as described here is practically impossible. To determine where the number 1.3662 comes from, we start with the equation of state for a perfect gas at constant volume and constant pressure, which yields

(1.93)

Next, constant‐volume and constant‐pressure thermometers are placed alternately in boiling water and melting ice, and the volume and pressure ratios of the gases in the devices (carbon dioxide CO₂, hydrogen H₂, and helium He) are measured at an initial pressure. If the procedure is repeated for different initial pressures and the results plotted versus pressure, straight lines are obtained, which converge at zero absolute pressure to a value of 1.3662, which must be the ratio of absolute temperature of boiling water and melting ice.

Currently, the international temperature scale (ITS‐90) is the standard used to represent the thermodynamic (absolute) temperature scale as closely as possible with improved accuracy over gas thermometry.