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Assume a reversible adiabatic process where is there no exchange of heat from cylinder to environment. I assume that the work done on the system will be equal to the work done by the system. So, the adiabatic compression and expansion will be similar to spring compression and expansion?

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I assume that the work done on the system will be equal to the work done by the system. So, the adiabatic compression and expansion will be similar to spring compression and expansion?

That's correct if you said the work done on the system by the surroundings will equal the negative of the work done by the system on the surroundings. Positive work on something transfers energy to that something. Negative work on something takes energy away from that something. The work is positive or negative depending on the direction of the force vs the direction of displacement. The magnitude of the positive work equals the magnitude of the negative work for conservation of energy.

For example, in an adiabatic expansion the system (gas) does positive work on the surroundings, transferring energy to the surroundings. At the same time the surroundings does an equal amount of negative work on the the system (gas), taking energy away from the system.

The same would apply to the work done by and on a spring during compression and extension.

Hope this helps.

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