Once again, using the KISS princilple, and reaching back (with apologies) to the dark recesses of my brain (some 38 years ago), I seem to remember the CFS 'simple' answer was to again draw two vertical columns, one high and hot and one low and cold.
Assume the same surface pressure and 'nothing' above the top of each column.
At any point, if you take a horizontal plane, the pressure in the hot will be greater than in the cold, since the air below is less dense, but the TOTAL weight of air in each column is the same.
As far as QNH calculations are concerned, we need a met man, but I ASSUME the pressure is adjusted at the standard lapse rate for pressure/1000' at the given OAT - and from a table? EG If the OAT was 12deg C at 1000', that would be pretty well ICAO, and I guess the 1mb/30 ft would apply? Given, therefore, a baro reading of 970mb there, I guess the 'QNH' would be 1003mb (ish)? (KISS again!). Sorry I cannot do that in inches, as they say
