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The wall is adiabatic and DeltaU=W(ad). ...

The wall is adiabatic and `DeltaU=W_(ad)`. What do you understand about the heat and work with respect to the system?

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In the adiabatic system neither matter nor energy is exchanged with the surroundings. So the wall will not allow the transmission of heat into surroundings or from the surroundings.
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