mma said:Could somebody tell me, how temperature of an ideal gas varies on height in homogeneous gravitational field in equilibrium?
I mean a gas column perfectly isolated from its environment.
No, thank you, the non-relativistic approach is enough for me. But this adiabatic approximation seems too heuristic for my taste.pervect said:If you are interested in exotic situations, relativistic effects may become important.
What is surprising, that concrete mathematical analysis also shows that (1) is the correct answer in the thermodynamical limit.If a vertical column
of an adiabatically enclosed ideal gas is in thermal
equilibrium, is the temperature the same throughout
the column or is there a temperature gradient along
the direction of the gravitational field? According to
Coombes and Laue, there are two conflicting answers
to the above question:
(1) The temperature is the same throughout because the
system is in equilibrium.
(2) The temperature decreases with the height because
of the following two reasons.
(a) Energy conservation implies that every
molecule loses kinetic energy as it travels
upward, so that the average kinetic energy of
all molecules decreases with height.
(b) Temperature is proportional to the average
molecular kinetic energy.
Coombes and Laue concluded that answer (1) is the
correct one and answer (2) is wrong.
An ideal gas is a theoretical concept used in physics and chemistry to describe the behavior of a gas at low pressure and high temperature. It is assumed to have particles with negligible volume and no intermolecular forces.
According to the Ideal Gas Law, an increase in temperature will cause an increase in the average kinetic energy of gas particles, leading to an increase in pressure and volume. This relationship is known as Charles' Law.
In a gravitational field, the volume of an ideal gas will decrease as the temperature increases. This is because the gas particles gain kinetic energy and collide more frequently, leading to a decrease in volume due to increased pressure. This relationship is known as Boyle's Law.
The gravitational field does not directly affect the temperature of an ideal gas. However, it does have an indirect effect by causing the gas to compress and expand, leading to changes in temperature due to changes in pressure and volume.
Studying temperature variations of an ideal gas in a gravitational field can help us understand the behavior of gases in different environments, such as on other planets or in outer space. It also has practical applications in fields such as engineering and meteorology.