adiabatic process
/ ay-dee-uh-BAT-ik /
An adiabatic process is one in which no heat crosses the boundary at all: Q = 0. The word comes from Greek for 'not passing through', meaning heat is not passing through the walls. This happens either because the system is wrapped in perfect insulation, or, more commonly, because the change is so fast that heat simply has no time to flow in or out. A bicycle pump warming up as you pump hard, or air cooling as it rises and expands into a cloud, are close to adiabatic.
With Q = 0 the first law ΔU = Q - W collapses to ΔU = -W. All the work now comes at the direct expense of internal energy: if the gas expands it does positive work, so its internal energy — and therefore its temperature — drops; if it is compressed, work is done on it, its internal energy rises, and it heats up. For an ideal gas an adiabatic path obeys P V^gamma = constant, where gamma (the ratio of heat capacities) is greater than 1, so an adiabat is steeper than the isotherm through the same point.
Adiabatic steps are the other half of the Carnot cycle and explain a great deal of weather: rising air expands and cools, which is why mountaintops are cold and why clouds form. The honest caveat is that 'no heat flow' is an idealization — some heat always leaks — but for fast processes it is an excellent approximation, and it is exactly right for a perfectly insulated system.
Compress air quickly in an insulated pump so that Q = 0. You do 300 J of work on the gas, so its work done is W = -300 J and ΔU = -W = +300 J: the internal energy rises by 300 J and the air gets noticeably hotter, even though no heat was added.
With no heat allowed in or out, compression heats a gas and expansion cools it.
Adiabatic (Q = 0) is not the same as isothermal (T constant) — they are almost opposites. In an adiabatic change the temperature is exactly what does change, because there is no heat flow to keep it steady.