Outrageous

The total work is the same in all adiabatic processes between any two equilibrium states having the same kinetic and potential energy.

That is another way to describe first law of thermodynamics , and define internal energy.
My question is what does "the same kinetic and potential energy " mean ?
Is that mean the kinetic energy of the gas system before adiabatic compression is same as kinetic energy of the gas system after adiabatic compression?
But I though when adiabatic compression, the temperature of the system will increase , and the kinetic energy will increase as well. Correct?


Thank you