Physics · Chapter 25
Study notes aligned to the official NEB syllabus.
A gas is the simplest state of matter to model because its molecules are far apart and interact only weakly. The ideal gas model treats a gas as a large number of point-like molecules in random motion, colliding elastically with each other and with the walls of the container. Real gases like hydrogen, oxygen and nitrogen behave very close to ideal at low pressure and moderately high temperature.
For a fixed mass of gas held at constant temperature, the volume varies inversely with pressure (Boyle's law):
$$PV = \text{constant} \quad (\text{constant } T, n)$$
For a fixed mass of gas held at constant pressure, the volume increases linearly with absolute temperature (Charles's law):
$$\frac{V}{T} = \text{constant} \quad (\text{constant } P, n)$$
A related form, sometimes called Gay-Lussac's law or the pressure law, holds the volume fixed and relates pressure to temperature:
$$\frac{P}{T} = \text{constant} \quad (\text{constant } V, n)$$
The temperature coefficients used in these laws (the pressure coefficient and the volume coefficient) both come out numerically equal to $\frac{1}{273.15}\ \text{K}^{-1}$ when temperature is measured from $0^\circ\text{C}$, which is the experimental basis for taking $-273.15^\circ\text{C}$ as the zero of the absolute scale.
If pressure (at constant volume) or volume (at constant pressure) is plotted against Celsius temperature for a real gas at low density, the graph is very nearly a straight line. Extrapolating that straight line backwards, it crosses the temperature axis (P = 0 or V = 0) at the same point for every gas: $-273.15^\circ\text{C}$.
The V-T version of this graph is shown below; a P-T graph at constant volume looks the same and extrapolates to the same point.
This temperature is called absolute zero, the temperature at which an ideal gas would (in principle) have zero pressure and zero volume, because molecular motion itself would cease. It defines the zero of the Kelvin scale: $T(\text{K}) = T(^\circ\text{C}) + 273.15$.
A gas is the simplest state of matter to model because its molecules are far apart and interact only weakly. The ideal gas model treats a gas as a large number of point-like molecules in random motion, colliding elastically with each other and with the walls of the container. Real gases like hydrogen, oxygen and nitrogen behave very close to ideal at low pressure and moderately high temperature.
For a fixed mass of gas held at constant temperature, the volume varies inversely with pressure (Boyle's law):
For a fixed mass of gas held at constant pressure, the volume increases linearly with absolute temperature (Charles's law):
A related form, sometimes called Gay-Lussac's law or the pressure law, holds the volume fixed and relates pressure to temperature:
The temperature coefficients used in these laws (the pressure coefficient and the volume coefficient) both come out numerically equal to when temperature is measured from , which is the experimental basis for taking as the zero of the absolute scale.
If pressure (at constant volume) or volume (at constant pressure) is plotted against Celsius temperature for a real gas at low density, the graph is very nearly a straight line. Extrapolating that straight line backwards, it crosses the temperature axis (P = 0 or V = 0) at the same point for every gas: .
The V-T version of this graph is shown below; a P-T graph at constant volume looks the same and extrapolates to the same point.
This temperature is called absolute zero, the temperature at which an ideal gas would (in principle) have zero pressure and zero volume, because molecular motion itself would cease. It defines the zero of the Kelvin scale: .