Question

I've been taught that temperature is the average kinetic energy of a particle. So when gas particles are heated, they move faster. This makes sense as an airplane traveling faster does make the nearby air warmer when measured from the plane.

Say I release a box of room temperature atmospheric pressured gas in the vacuum of space. Assuming there is no gravity, all the gas particles will be traveling in a straight line as they won't be bumping into other particles. And since space is only a few degrees above absolute zero, the gas particles will cool down after they transferred a lot of their thermal energy via radiation, and thus should slow down (lower temperature = lower speed). Looking at a single gas particle this breaks the conservation of momentum, as it is quite literally slowing down to nothing. So what's going on.

Now imagine there is indeed gravity in space, the gas particles will eventually start traveling and be accelerated toward a source of gravity. So its kinetic energy increases and so does its temperature (higher speed = higher temperature). First of all it is heated up by nothing without any sort of heat transfer taking place, and would there be any distinction between temperature and speed? Why does this only seem to apply to gas and not solids - a fast moving car wouldn't look hotter would it (ignore friction with air).

Answer 1

In the vacuum of space, gas particles released at room temperature and atmospheric pressure will undergo a process called adiabatic cooling, where they lose thermal energy via radiation. As a result, their average kinetic energy decreases, leading to a decrease in temperature and speed. In the presence of gravity, the particles will be accelerated, gaining kinetic energy and experiencing an increase in temperature and speed. The distinction between temperature and speed is maintained, with temperature being a measure of average kinetic energy and speed reflecting the individual particle's velocity.

Step-by-step explanation

In the vacuum of space without gravity, gas particles initially move in a straight line, but they undergo adiabatic cooling as they radiate thermal energy into the cold void. Adiabatic cooling occurs when a gas expands without heat transfer, leading to a decrease in temperature. This process is governed by the ideal gas law, where the product of pressure (P) and volume (V) raised to the adiabatic index (γ) remains constant. The decrease in volume results in a decrease in temperature and speed.

When gravity is present, gas particles are subject to gravitational acceleration. As they fall toward a gravitational source, their kinetic energy and temperature increase. The increase in kinetic energy is a result of the work done by gravity on the particles, converting potential energy to kinetic energy. This rise in kinetic energy corresponds to an increase in temperature, following the relationship between kinetic energy, temperature, and speed. Importantly, the distinction between temperature and speed remains valid; temperature represents the average kinetic energy of the particles, while speed reflects the individual particles' velocities.

In summary, the behavior of gas particles in space without gravity involves adiabatic cooling, leading to a decrease in temperature and speed. In the presence of gravity, particles experience an increase in temperature and speed due to gravitational acceleration, maintaining the fundamental distinction between temperature and speed in the context of gas dynamics.