Posted by phys on Tuesday, April 27, 2010 at 12:44am.
The answer to your question is "no". Pressure decreases by a larger factor than the volume increases in an adiabatic expansion. The net result is that the temperature also decreases.
PV = nRT is always correct for ideal gases.
In an adiabatic process, P, V and T all vary, but in such a way that no heat is added or removed. Work is done by a gas when it expands into a surrounding gas. This requires that the temperature of the gas drop.
There can be both adiabatic expansions (during which the gas temperature and pressure both decrease) and adiabatic compressions (during which the temperature and pressure both increase.)
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