You might find this device interesting: https://en.wikipedia.org/wiki/Vortex_tube https://en.wikipedia.org/wiki/Vortex_tube It does take energy to separate th

You might find this device interesting: https://en.wikipedia.org/wiki/Vortex_tube https://en.wikipedia.org/wiki/Vortex_tube It does take energy to separate the hot and cold air - the incoming mixed air is at a high pressure while the outgoing separated air is at normal pressure.