Definition of state function:-

                                                The thermodynamic property of a system which is depend upon initial and final state and does not depend upon the path followed by the system is known as state function. Example: - Temperature, pressure, volume.

Explain internal energy is a State Function

 Internal energy:-

                        The sum of all form of energy associated with matter present in the system is called internal energy of a system. 

SOLUTION :

                            Consider system A having Internal energy U₁ , pressure P₁ and Volume V₁ ( initial state ) and system B having Internal energy U₂ , pressure P₂ and Volume V₂ ( final state )Suppose that change in state A to state B along Path I.

             

           Change in internal energy along path A is (pathI)

                        ΔU (path I) =  U₂  - U₁

     Again consider that change in state B to State A along path II

             Change in internal energy along path B is (pathII)

                        ΔU(path II) =  U_{1 -} U₂

                        ΔU = ΔU (path I) + ΔU( path II )

                         ΔU    = (U₂  - U₁ ) +( U_{1 -} U₂ )

ΔU    = (U₂ - U₂) + (U₁ - U₁ )

                          ΔU    =   0

From the above equation we can say that internal energy is state function.