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In the high-pressure area it is mostly likely that there is sun. In low pressure area it is mostly likely that rain will occur.

Because of the law that p * V = (c) * T where p is pressure, V is volume, T is temperature and (c) is a constant value, for the same T temperature, lowering pressure p should lead to increase volume of the gas (air in this example).

Ant vice versa: lowering volume V leads to increase p pressure. The gas should be guided to condensation and the rain.

So using this basic formula high pressure area should be more likely to cause rain.

Where am I thinking wrong? Are there too many simplifications?

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The processes of condensation in atmospheric weather systems are much more complicated and can not be modeled by the ideal gas law, which is BTW as the name says only valid for an ideal gas which consists of non-interacting constituents, which means in an ideal gas no condensation can happen. –  Dilaton Jun 4 '13 at 14:54
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3 Answers

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Generally speaking low and high pressure areas are associated with vertical movement of the air. Air rises in a low pressure area and falls in a high pressure area. In a low pressure area the rising air cools and this is likely to condense water vapour and form clouds, and consequently rain. The opposite is true in a high pressure area, which is why high pressure tends to give cloudless skies.

However, you should also note that low pressure areas tend to be associated with weather fronts, and these (especially cold fronts) also cause rain.

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Why does air go up? Because it's getting warm, right? So why if it's cooling doesn't it just go down but condenses to rain? –  Voitcus May 20 '13 at 21:02
    
You can get thermal lows, where the low pressure is caused by hot air rising. However in the UK low pressure is normally associated with the air flow at fronts. See en.wikipedia.org/wiki/Pressure_system#Low-pressure_system of weatherquestions.com/What_causes_low_pressure.htm is a more accessible description. –  John Rennie May 21 '13 at 7:01
    
Now I understand. Thanks to you and David too. –  Voitcus May 21 '13 at 19:30
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An increase in pressure is not what causes condensation and rain.

Besides, the formula $pV = \text{const}$ applies to an isolated sample of a fixed amount of gas at a fixed temperature. Those conditions don't hold true for air in the atmosphere.

The real reason it rains is quite complicated, but the gist of it is that upward air currents can carry air with a high concentration of water vapor from near the surface into the upper atmosphere. As this happens, the air's temperature drops because of the reduced pressure and also because of heat loss to the colder surrounding air. When the air gets cool enough, the water condenses out and may fall as rain. These upward air currents produce low pressure as a side effect.

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But shouldn't cool air just go down? –  Voitcus May 20 '13 at 21:03
    
Cool air has a slight tendency to drop, yes, but it is easily overwhelmed by other effects. The reason the air is cooler at higher altitudes is that air is heated by the ground. –  David Z May 20 '13 at 21:13
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The atmosphere is a mixture of dry air and water vapour, where the content of the latter may vary. Water vapour is lighter than air, hence a vertical column of this gaseous mixture will weigh less (i.e. cause less pressure) when there is more water vapour. When atmosperic temperature is constant in horizontal directions, low pressure means (is caused by) more water vapour in the atmopshere. When there is more water vapour the chance of rain is higher. Starting from here one may add the already mentioned effects of vertical rise of the air and water vapour.

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