Q:

Are certain isobar temperatures higher in mountainous regions?

So we know that the air temperature at higher elevations is lower. But is the air temperature at a certain isobar over, say Vail, Colorado, higher than the air temperature of the same isobar over, say, New York City?
And more importantly, do these differences in air temperature along the same isobar affect the large-scale atmospheric circulation?

A:

Well, if there were no other factors, the temperature at the same isobar should be the same all over the Earth. But there are other factors, like winds, air mixing, albedo, ocean currents etc.
The temperature in atmosphere is lower at higher altitudes. That's because the air is gas, and it compresses. So the air at ocean level is denser than the air at 10km height. The air heats from the ground, and when it's getting warmer, it goes up. But because there is lower pressure, it expands, and while it's expanding, it cools down. That's why the higher you go - the colder it is. But if the pressure is not changing, the temperature shouldn't change too.

