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In isothermal the temperature is constant whereas in adiabatic the temperature falls or rises rapidly.Consider the case for expansion where in adiabatic the temperature drops. If you consider PV/T=constant then for same pressure we can show that as temp decreases the volume also decreases. During expansion for isothermal the temp does not change so volume is higher than adiabatic.

Example:

Isothermal P=8 Pa, V=x , T=2K

Adiabatic P=8 Pa, V=y, T=1K (as it drops)

Using PV/T=constant we can find that y is less than x.

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