State function and Path function

State Function:

  • In thermodynamics, a state function, state quantity, or a function of the state, is a property of a system that depends only on the initial and final state the system, not on the way in which the system acquired that state.
  • A state function describes the equilibrium state of a system and thus also describes the types of system.
  • The cyclic integral involving a state function is always zero.
  • All the thermodynamics property satisfy the requirements of state function.
  • U = q + w         change in thermodynamic energy
    S = qrev/T            entropy
    H = U = PV         enthalpy
    G = H – TS          Gibb’s free energy
    A = U – TS          Helmholtz free energy
  • Internal energy, enthalpy, entropy are the example of state functions.

Path Function:

  • Path function depends on the path taken to reach that specific value, not on the initial and final state of that value.
  • Path function needs multiple integral and limits of the integration in order to integrate.
  • It is based on how the state of a system was established.
  • Work, heat, arc length are the example of path function.

Thermodynamic process

Thermodynamic process:

        It is the path or operation by which a system changes from one state to another state.

1. Isothermal process: 

        The temperature of the system remains constant during each step.
        T = constant => dT = 0


  • For such change system should be contained in a perfectly conducting container.
  • Perfect isothermal change is impossible but when a change is carried out very slowly approximate isothermal change occurs.
  • It follows Boyle’s law.
  • Work done in the isothermal process is graphically given by the area under the P-V curve.
  • ∆H = nCp∆T  and  ∆H = nCv∆T
              In isothermal process ∆T = 0
                                             => ∆H = 0 and ∆E = 0
  • Specific change at constant T is infinitely great in the isothermal process.

2. Adiabatic process:

        There is no heat exchange between the system and surroundings.
             q = constant
        => dq = 0
        Perfectly adiabatic change is impossible but when a process is carried out very rapidly fairly
        approximate adiabatic change occurs.

3. Isobaric process:

              It is the system in which pressure of the system remains constant during each step.
              P = constant , dp = 0

4. Polytropic process:

         In this process heat capacity of the body remains constant.
            Cp = constant  and  Cv = constant

       => dCp = 0  and  dC = 0

5. Quasistatic process:

         The process in which the deviation from thermodynamic equilibrium is infinitesimal and all the states through which the system passes can be considered as equilibrium states.

6. Isochoric process :

         When there is no change in the volume of the system during various operations the change is said to be isochoric.
       V = constant  => dv = 0
    For example, the combustion of a substance in a bomb calorimeter is an isochoric process.

7. Cyclic process:

           The process which brings back a system to its original state after a series of changes is called acyclic process.
   As the E and H depend only on their states, E and H are constant.
   So, dE = 0 and  dH = 0

Reversiable and Irreversiable process

Reversible Process:

                   A thermodynamically reversible process is one in which all the changes occurring in any part of the process are exactly reversed when it is carried out in opposite direction.

Characteristic of the reversible process:

  • It has to be carried out in infinitesimal amount and hence require infinite time. Therefore changes in this process are very slow.
  • At all time during the process, the driving force for the change is opposed by a restraining force infinitesimally smaller than the driving force.
  • It can be reversed by an infinitesimal increase in opposing force.
  • The work produced in the reversible process is maximum.

Irreversible process:

                The process which occurs suddenly or spontaneously without the restriction of occurring in the successive stage of infinitesimal quantities.

Characteristic of the irreversible process:

  • In an irreversible process work done in the forward direction and in the backward direction are not equal.
  • If the initial and final stages are specified, the internal energy change would always be the same, whether the process has been affected by reversibly or irreversibly.
  • In an irreversible process, since the work done(dw) in two opposite direction are unequal, the heat transfer(dq)would also be unequal.
  • All the natural processes are irreversible.
                   e.g.=>  (1) flow of heat from high temperature to low temperature
                               (2) expansion of gas from high pressure to low pressure