Question

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When the temperature of air in an open region increases:

Answer 1

Since we are considering air in an open region, there is no constraint on change of its volume. Therefore, the air will expand with increasing temperature. This will cause the density of air to reduce. This, in turn, will cause the hot air to rise up in the atmosphere. This upward movement of air actually tends to create the partial vacuum and thus reduces the air pressure (less dense) at places which are hotter.

In other words, warm air region will be less dense and will be at low pressure as the amount of air will be less per unit area compared to less warm air region.