Work done is not a state function

Prove that Work done is not a state functions but it a path functions.

Definition:

The function which is depending upon the path is known as path function.

              Consider a system that goes from Initial state where volume is V₁ to the final state where volume is V₂ by three different paths.

i)   Path I :- The system is allowed to expand freely in vacuum  from volume V₁ to V₂

 W = 0   ------------ 1

ii)   Path II :- The system is allowed to expand from volume V₁ to V₂  against const. external  pressure at const temperature  

                                                 W = - P_ext ∆V

                                                    = - P_ex (V₂ – V₁)

iii  Path III:- The system is expand from volume V₁ to V₂ under reversible isothermal condition

                                                 W_max  = - 2.303nRT log₁₀V₂ /V₁

                   Thus the amount of work done is different for three different path where Initial and final state are same. Hence the work done is depending upon the path hence it is path function. 

Unit of energy and Work

                   The unit of energy is Joule (J) named after James Joule who made a study of heat and Work in the nineteenth century

                   1J = 1Kg m²/s²

Sr.No	To from	Lit atm	Erg	Calories	Joule
1	Lit atm	-	1.33 X 107	24.22	101.28
2	Erg	9.871 X10-10	-	2.390 X 10-8	1 X 10-7
3	Calories	4.132 X10-2	4.184 x 107	-	4.184
4	Joule	9.869 X 10-3	1 X 107	0.239	-

Note: - Any energy that enters the system from the surrounding has a positive value and leave the system and flow to the surrounding has negative value.

          Positive value of W or q. signifies that the energy is supplied to the system as work or Heat

          A negative value of w or q signifies that the energy is left the system as work or Heat.

Internal energy:-

          Internal energy is the sums of all forms of energy associated with the substance present in system known as internal energy. It is indicated by U

          Total internal energy = kinetic energy + potential energy.

The absolute value of internal energy cannot be determined but change in internal energy can be determined 

 The change in internal energy is given by  

 ∆U = U₂ – U₁

Where    U₁ is the internal energy of system in initial state.  

               U₂ is the internal energy of system in final state.

Internal energy is a state function means depending upon initial state and final state of system

Internal energy is changed as the energy transfer in and out of the system as Work or Heat.

Case 1 – When energy is transfer into the system by heating or doing work on it then energy is added to the system then internal energy increase.

Case 2- When energy is transfer from the system by cooling or doing work on surrounding then energy is released from the system then internal energy is decreases.

Example: I) If a 20KJ of work is done on the system then it is added to the system then internal energy is increased by 20KJ and ∆µ = + 20KJ.

II) If 10KJ of heat supplied to the system by heating, the heat is added to the then internal energy is increased by 10KJ Therefore ∆U = + 10KJ.

III) If 15KJ of heat is released by the system as energy and 10KJ of work is done on surrounding then internal energy decreased ∆U = (- 15- 10) = -25KJ

IV) If 25 KJ work is done on the system and 15KJ is heat Released then change

                             ∆U = 25 – 15 = + 10KJ

Note :-> Work done on the system (by the surrounding) = increased in internal energy Heat is supplied or absorbed

Work done by the system (on the surrounding) = decreased in internal energy (heat is released or librated)

          Note :->     ∆U= kinetic energy + potential energy

                             =(Thermal energy) + (Bonding energy)

                            =  (U_trans + u_vib + U_rot+ U_ele) + (U_intra + U_inter )

U_ele = negligible

        (U_trans + U_vib + U_rot) + (U_intra + U_intra  )