Hot to Cold look out below
I read this forum but still am a little uncertain why the statement "Hot to cold look out below" is true. It seems contrary to what you would expect. I don't think the PHAK explains it very well or at least I am not getting it. There was an illustration previously posted from the PHAK above but I would like to make sure my interpretation of the illustration is correct.
Is it because in colder air, the pressure decreases with altitude more abruptly (faster rate) resulting in a "tighter stack" of pressure change? Therefore when encountering colder air, you will descend to stay at the same indicated altitude? That makes sense to me but I am not sure if it is correct.
The PHAK's explanation is that this occurs because cold air is more dense but I am not sure that really explains it.