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A piston is pressed down to compress the air trapped inside. Then the piston is allowed to come to thermal equilibrium with the room. Describe the energy transfer process?

The answer to this problem is "work is done on the gas by the piston, then heat leaves the gas," which makes sense but my response was "work is done on the gas by the piston, then work is done by the gas to bring it to room temperature." Why is my answer incorrect? When you push a piston against the gas, doesn't the gas push back, causing it to do work and cool?

The answer to this problem is "work is done on the gas by the piston, then heat leaves the gas," which makes sense but my response was "work is done on the gas by the piston, then work is done by the gas to bring it to room temperature." Why is my answer incorrect? When you push a piston against the gas, doesn't the gas push back, causing it to do work and cool?

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