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yes since it is law of energy balance so irrespective of the process it can be applied to any process but small change comes when we deal with reversible and irreversible processes.

it can be explained in text form :

please give attention to the text;

CHANGE IN TOTAL ENERGY( it is sum of change in macroscopic kinetic energy and change in macroscopic potential energy and change in internal energy,U) = HEAT TAKEN BY THE SYSTEM {actually heat taken by the medium which we use often an ideal gas}(sum of heat given to the system from outside+ heat generated with in the system ) + WORK DONE BY THE MEDIUM OR SYSTEM {again it includes all kind of works such as expansion work shaft work electrical work etc. also when the process is IRREVERSIBLE it includes internal work which is consumed to overcome the friction}

for reversible processes there is no dissipation of internal heat and internal work in that case we consider that the piston cylinder which we use to explain first law is frictionless . and also since they have a characteristic property of INFINITE SLOWNESS the reversible process can be considered at equilibrium at each state.

For irreversible processes the heat is generally generates with in the system because we do not use the friction less piston cylinder arrangement.

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