Temperature and pressure
Can someone offers an explanation of how temperature affects pressure in the free atmosphere? A book I am reading says a cold front brings "A sharp fall in temperature, a rise in presure." But searching online I found some places describing an increase in temperature brings a rise in pressure.
There are two theories that appears to contradict:
1) A hot area heats up the air above it and lifts this, causing the surrounding air to flow into this area of "low" pressure.
2) A hot area lifts the air above it, expanding this column of air. So if you are at 1,000 ft measuring the pressure, the station pressure should reflect an increase in pressure with more air molecules rising above you over time.
Is there a book that can provide a very good explanation of temperature and pressure? Better if it utilizes math. And also explanation of the conversion, especially the reduction part, of the Qs (ie QNE, QNH, QFE, etc)
Thanks.