When the kinetic energy of a fluid increases as it is accelerated in an adiabatic nozzle., the energy comes from its internal energy.
The definition of an adiabatic process is the thermodynamic process in which neither during expansion nor compression does heat from the system transfer to its surroundings. Either the adiabatic process is reversible or it is irreversible.
As in adiabatic process no energy is transferred with surroundings, when the kinetic energy of a fluid increases, its internal energy decreases. That's why during a fluid is accelerated in an adiabatic nozzle, it is cold down and internal energy decreases.
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