Second law of thermodynamics and enthalpy

Second law of thermodynamics:-

Statements:-

1)   The spontaneous flow of heat is always unidirectional from higher temperature to lower temperature.

2)   The heat cannot be completely converted into the equivalent amount of work without producing permanent changes either in the system or its surrounding.

3)   No machine has yet been made that has efficiency unity.

ENTHALPY

Definition: -

        It is defined as the sum of internal energy and pressure, volume type energy. Denoted by H.

Mathematical expression:-

                             H = U + PV

Since U, P, V is state function hence H is also state function

Therefore ∆H = H₂ – H₁

Where H₁ is enthalpy of system in initial state

              H₂ is enthalpy of system in final state

          H₁ = U₁ + P₁ V₁

H₂ =  U₂+ P₂ V₂

  ∆H = H₂ – H₁

  ∆H = U₂+ P₂ V₂  - (U₁ + P₁ V₁)

  ∆H = U₂- U₁ + P₂V_{2 -} P₁V₁

At constant pressure P = P₁ = P₂

  ∆H = ∆U + P ∆V                               -------------1

            q_P = ∆U + Pex ∆V        ( Isobaric process) 

Assuming that P_ex = P

           q_P = ∆U + P∆V                                   ------------2

Compare equation   1 & 2

           ∆H = q_P

Increase in enthalpy of system is equal to heat absorbed by it when reaction is carried out at constant pressure

Relationship between ∆H and ∆U for chemical reaction

          We known that

                   ∆H = ∆U + P ∆V

For reaction involving solid and liquid ∆V is neglected because it is not expand

 P∆V is neglected

Hence ∆H = ∆U

For reaction involving gases ∆U is not neglected 

                    ∆H = ∆U + P∆V

                        = ∆U + P(V₂  - V₁)

                        = ∆U + (PV₂ - PV₁)

Where  V₁ = volume of reactant in initial state

             V₂ = volume of reactant in final state

Assuming ideal behaviors of gas

          PV = nRT

  n₁ = No. of mole of gases Reactant

  n₂ = No. of mole of gases product

          PV₁ = n₁ RT

          PV₂ = n₂ RT

          ∆H = ∆U + n₂ RT - n₁ RT

          ∆H = ∆U + RT (n₂  - n₁)

          ∆H = ∆U + RT ∆n

Where, ∆n is difference between No. of mole of gases product and gases Reactant

 ∆H = change in enthalpy

 R = gas constant

 T= Temperature  

 ∆U = increases in internal energy.

Expression for Work done in chemical Reaction:-

          We known that

                             W = -Pex ∆V

Assuming Pex = P

                             W = -P∆V

                             W = - P (V₂  - V₁)

                                 =  PV₂  -  PV₁

                                 = - ( PV₂   +  PV₁  )

Again          PV = nRT

                             PV₁  = n₁ RT

                             PV₂  = n₂ RT

                             W = - (n₂ RT + n₁ RT)

                              W = -RT (n₂ -  n₁)

                              W = -RT ∆n -----------------1

Equation   1 gives work done by the system in chemical reaction

i)     If n₂ > n_{1 ,}W is negative & work is done by the system on surrounding

ii)    if n₂ <n₁, W is positive &work done on the system by surrounding

iii) if n₂ = n_1,W= 0, no work is done