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A gas does work during adiabatic change. What is the source of mechanical energy to produced?

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For an adiabatic change, the first law of thermodynamics may be expressed as 

dU + PdV = 0

or,  −PdV = dU …(i)

When a gas does work adiabatically PdV is +ve. For this dU should ne negative. Hence, the source of mechanical energy produced during the adiabatic change is the decrease in internal energy of the gas.

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