Simple Nature - Light and Matter

h / A simplified version of anideal gas thermometer. Thewhole instrument is allowed tocome into thermal equilibriumwith the substance whose temperatureis to be measured, andthe mouth of the cylinder is leftopen to standard pressure. Thevolume of the noble gas gives anindication of temperature.i / The volume of 1 kg of neongas as a function of temperature(at standard pressure). Althoughneon would actually condenseinto a liquid at some point,extrapolating the graph givesto zero volume gives the sametemperature as for any other gas:absolute zero.solids or liquids, and the noble gases like helium and neon are moreconsistent with each other than gases in general. Continuing tosearch for consistency, we find that noble gases are more consistentwith each other when their pressure is very low.As an idealization, we imagine a gas in which the atoms interactonly with the sides of the container, not with each other. Such agas is perfectly nonreactive (as the noble gases very nearly are), andnever condenses to a liquid (as the noble gases do only at extremelylow temperatures). Its atoms take up a negligible fraction of theavailable volume. Any gas can be made to behave very much likethis if the pressure is extremely low, so that the atoms hardly everencounter each other. Such a gas is called an ideal gas, and we definethe Celsius scale in terms of the volume of the gas in a thermometerwhose working substance is an ideal gas maintained at a fixed (verylow) pressure, and which is calibrated at 0 and 100 degrees accordingto the melting and boiling points of water. The Celsius scale is notjust a comparative scale but an additive one as well: every step intemperature is equal, and it makes sense to say that the differencein temperature between 18 and 28 ◦ C is the same as the differencebetween 48 and 58.Absolute zero and the kelvin scaleWe find that if we extrapolate a graph of volume versus temperature,the volume becomes zero at nearly the same temperaturefor all gases: -273 ◦ C. Real gases will all condense into liquids atsome temperature above this, but an ideal gas would achieve zerovolume at this temperature, known as absolute zero. The most usefultemperature scale in scientific work is one whose zero is definedby absolute zero, rather than by some arbitrary standard like themelting point of water. The temperature scale used universally inscientific work, called the Kelvin scale, is the same as the Celsiusscale, but shifted by 273 degrees to make its zero coincide with absolutezero. Scientists use the Celsius scale only for comparisons orwhen a change in temperature is all that is required for a calculation.Only on the Kelvin scale does it make sense to discuss ratiosof temperatures, e.g., to say that one temperature is twice as hot asanother.Which temperature scale to use example 6⊲ You open an astronomy book and encounter the equation(light emitted) = (constant) × T 4for the light emitted by a star as a function of its surface temperature.What temperature scale is implied?⊲ The equation tells us that doubling the temperature results inthe emission of 16 times as much light. Such a ratio only makessense if the Kelvin scale is used.304 Chapter 5 Thermodynamics