Lesson 2 of 13 · 6 min
Ideal-gas equation and absolute temperature
NCERT §10.4
On the drive up, Tara's packet of chips puffs up like a pillow as the car climbs, and at a cold dawn stop the car's tyre gauge reads lower than it did in Chennai. Gases react to pressure and temperature far more than solids do, and that makes them the most dependable thermometers.
The lesson in notes
In short
Liquid-in-glass thermometers made with different liquids agree at the fixed points but can disagree in between, because the liquids expand differently. A gas thermometer reads the same whichever gas it holds, since all gases at low density behave alike.
Boyle's law (Robert Boyle, 1627–1691): at fixed temperature, PV = constant for a given amount of gas at low density.
Charles' law (Jacques Charles, 1747–1823): at fixed pressure, V/T = constant.
The two combine into the ideal-gas equation PV = μRT. Here μ counts moles of gas, and R = 8.31 J mol⁻¹ K⁻¹ is the universal gas constant.
A constant-volume gas thermometer uses the pressure of a fixed volume of gas: P ∝ T. Real gases liquefy at low temperature, but the straight P–t lines extended backwards all reach P = 0 at one temperature.
That temperature, −273.15 °C, is absolute zero. It is the basis of the Kelvin scale, named after Lord Kelvin, on which the triple point of water is 273.16 K.
A kelvin and a degree Celsius are the same size, so a temperature difference has the same value in both. Only the zero differs: T = t_C + 273.15.
So 0 °C = 273.15 K and 100 °C = 373.15 K; in rough work the 0.15 is often dropped.