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In an adiabatic system, there is no heat transferred; therefore, the total change in internal energy of the system is equal to the work performed (deltaU=w). In an isothermal system, there's no change in temperature; therefore, the total internal energy of the system doesn't change (deltaU=0). Because of this, the heat transferred is equivalent in value to the work performed (q=-w) for isothermal.
They pertain to solving for change in U, as in Isothermic conditions there is no change in temp. but work is done equivalent to -q which is the change in U. For adiabatic conditions there is no heat transferred. Basically under both conditions keep in mind that q=0.
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