Mail Time! -- adiabatic vs. isothermal process

Reader Elizabeth Walker writes:

"I have trouble telling the difference between an isothermal process and an adiabatic process on the graph. What am I missing?"

The Nachoman responds:

In an isothermal process the product of PV will be the same everywhere. An adiabatic process will drop below the isothermal process (assuming expansion). Why? Because ΔU = Q + W. An adiabatic process MEANS no heat added or removed, thus Q = 0.

The gas expands, so work is done BY the gas. That means the variable W is negative. By the first law, then, ΔU must also be negative... meaning the temperature of the gas must decrease. The product of PV will be smaller as the gas expands, meaning that the adiabatic process drops below the isothermal process on the PV diagram.

GCJ