2 math formatting edited Nov 14 '15 at 6:58 DanielSank 18.7k44 gold badges5757 silver badges8383 bronze badges An example of a difference where the pressure of a reasonably dilute gas depends on something else other than the kinetic energy of the particles is actually just the air on Earth. A classic exercise in statistical mechanics is to consider an ideal gas subject to gravity and find how the pressure varies with altitude. Of course, in reality the temperature of the air on Earth varies with altitude, but doing this problem by assuming that the gas has a constant temperature provides a pretty reasonable result, that the pressure goes as $$P(z) \sim e^{-\frac{mgz}{kT}}$$$$P(z) \sim \exp\{-mgz/kT\}$$ (don't quote me on this) where m$$m$$ is mean molecular mass. In this case, to a decent approximation, the pressure of the gas varies with height, but the temperature does not, because one now takes into account the gravitational potential and not just the kinetic energy. An example of a difference where the pressure of a reasonably dilute gas depends on something else other than the kinetic energy of the particles is actually just the air on Earth. A classic exercise in statistical mechanics is to consider an ideal gas subject to gravity and find how the pressure varies with altitude. Of course, in reality the temperature of the air on Earth varies with altitude, but doing this problem by assuming that the gas has a constant temperature provides a pretty reasonable result, that the pressure goes as $$P(z) \sim e^{-\frac{mgz}{kT}}$$ (don't quote me on this) where m is mean molecular mass. In this case, to a decent approximation, the pressure of the gas varies with height, but the temperature does not, because one now takes into account the gravitational potential and not just the kinetic energy. An example of a difference where the pressure of a reasonably dilute gas depends on something else other than the kinetic energy of the particles is actually just the air on Earth. A classic exercise in statistical mechanics is to consider an ideal gas subject to gravity and find how the pressure varies with altitude. Of course, in reality the temperature of the air on Earth varies with altitude, but doing this problem by assuming that the gas has a constant temperature provides a pretty reasonable result, that the pressure goes as $$P(z) \sim \exp\{-mgz/kT\}$$ (don't quote me on this) where $$m$$ is mean molecular mass. In this case, to a decent approximation, the pressure of the gas varies with height, but the temperature does not, because one now takes into account the gravitational potential and not just the kinetic energy. 1 answered Nov 14 '15 at 6:43 seal 3133 bronze badges An example of a difference where the pressure of a reasonably dilute gas depends on something else other than the kinetic energy of the particles is actually just the air on Earth. A classic exercise in statistical mechanics is to consider an ideal gas subject to gravity and find how the pressure varies with altitude. Of course, in reality the temperature of the air on Earth varies with altitude, but doing this problem by assuming that the gas has a constant temperature provides a pretty reasonable result, that the pressure goes as $$P(z) \sim e^{-\frac{mgz}{kT}}$$ (don't quote me on this) where m is mean molecular mass. In this case, to a decent approximation, the pressure of the gas varies with height, but the temperature does not, because one now takes into account the gravitational potential and not just the kinetic energy.