Enthalpy (H) Introduction : Heat change in isochoric process and isobaric process :

The thermal changes taking place at a constant volume (Isochoric Process) are conventionally expressed in terms of internal energy. 

Whereas the thermal changes taking place at a constant pressure (Isobaric Process)  are expressed in terms of  another function ‘H’ called the heat content of the system or enthalpy.

 

Enthalpy is expressed as  H = E + pV.

Enthalpy is a state function  and  Extensive properties 

Molar Enthalpy: Heat absorbed by the mole substance at constant pressure  and it is Intensive properties.  (H = E+PV ) 

Absolute value of Enthalpy can not calculated but we can calculate only change in enthalpy.

We known 1^st law of thermodynamics (FLOT)

                                        dU=dq+dW 

  If P_ext = constant (Isobaric Process)

  Then dW= - PdV

     and     dU= dq - PdV

                dq=dU-PdV

                dq=(U₂-U₁)+P(V₂-V₁)

                dq=(U2+PV2)-(U1+PV1)

                dQ=H2-H1                            ( H₂=U₂+PV₂  and H₁=U₁+PV₁)

                dq=dH

Hence the enthalpy of a system is defined as:

                                               H = U + PV

                                             DH = DU + D(PV)

Where

H is the enthalpy of the system

U is the internal energy of the system

P is the pressure at the boundary of the system and its environment.

(1) In thermodynamics the quantity U + PV is a new state function and known as the  enthalpy of the system and is denoted by H=U+PV. It represents the total energy stored in the system.

(2) It may be noted that change in enthalpy is equal to heat exchange at constant pressure.

(3) Enthalpy is also an extensive property as well as a state function.                                

(4) The absolute value of enthalpy cannot be determined, however the change in enthalpy can  be experimentally determined.

               DH = DU + D(PV)

(5) Change in enthalpy is a more useful quantity than its absolute value.

(6) The unit of measurement for enthalpy (SI) is joule.

(7)The enthalpy is the preferred expression of system energy changes in many chemical and physical measurements, because it simplifies certain descriptions of energy transfer. This is because a change in enthalpy takes account of energy transferred to the environment through the expansion of the system under study.

(8)The change dH is positive in endothermic reactions, and negative in exothermic processes. dH of a system is equal to the sum of non-mechanical work done on it and the heat supplied to it.

(9) For quasi static processes under constant pressure, dH is equal to the change in the internal energy of the system, plus the work that the system has done on its surroundings. This means that the change in enthalpy under such conditions is the heat absorbed (or released) by a chemical reaction.

NOTE:

Transfer of heat at constant volume brings about a change in the internal energy(DU) of the system whereas that at constant pressure brings about a change in the enthalpy (DH) of the system.

For Ideal gas

                     H=U+PV   and U=f(T)

                     PV=nRT

                    H=U+nRT   and H=f(T) only for ideal gas

For other substance and real gas

                     H=U+PV  

                     U=f(P,V,T) and H=f(,PV,T)

       So         H=f(P,T)/ f(V,T)/ f(P,V)

H=f(T,P)

           dH=(dH/dT)_p dT+(dH/dP)_T dP------------------------------------- (1)

H=f(V,T)

           dH=(dH/dV)_T dV+(dH/dT)_V dT------------------------------------- (2)

H=f(P,V)

           dH=(dH/dV)_P dV+(dH/dP)_V dP------------------------------------- (3)

Out of the above three relation H as function on of (T,P) Has a greater significance. The above differential equation simplified for different substance for different condition.

For isobaric process : dP = 0 (Molar Heat capacity at constant Pressure)

We known

                 Q_P=nC_pmdT (Molar Heat capacity at constant Pressure)

                 C_pm= (dQ/dT)_P   for 1 mole of gas

                            dQ=dH  at dP=0

   then         C_pm= (dH/dT)_P  

         

For an ideal gas: change in enthalpy at constant temperature with change in

pressure is zero. i.e.

Continue...........

RELATIONSHIP BETWEEN DH AND DU