Enthalpy of a System

The quantity U + PV is known as the enthalpy of the system and is denoted by H. It represents the total energy stored in the system. Thus

      H = U + PV

It may be noted that like internal energy, enthalpy is also an extensive property as well as a state function. The absolute value of enthalpy can not be determined, however the change in enthalpy can be experimentally determined.

      ΔH = ΔU + Δ(PV)

Various kinds of processes:  

(i) Isothermal reversible expansion of an Ideal gas: Since internal energy of an Ideal gas is a function of temperature and it remains constant throughout the process hence  

ΔE = 0 and ΔH = ΔE + ΔPV  

            ΔE = 0  

            and P1V1 = P2V2 at constant temperature for a given amount of the gas  

            ΔH= 0  

Calculation of q and w:  

ΔE = q + w  

For an Isothermal process, w = -q  

This shows that in an Isothermal expansion, the work done by the gas is equal to amount of heat absorbed.  

            and w = - n RT ln(V2/V1) = - n RT ln(P1/P2).  

Solved examples.10 gm of Helium at 127°C is expanded isothermally from 100 atm to 1 atm Calculate the work done when the expansion is carried out (i) in single step (ii) in three steps the intermediate pressure being 60 and 30 atm respectively and (iii) reversibly.  

Solution:       (i)  Work done = V.ΔP  

                              V = (10/4) × 8.314×400 / 100 × 105 = 83.14 × 10–5 m3   

                              So W = 83×14/105 (100-1) × 10=  8230.86 J.  

                   (ii) In three steps  

                              VI = 83.14×10-5 m3  

                              WI = (83.14×10-5)´(100-60)×105  

                                  = 3325.6 Jules  

                              VII = 2.5 × 8.314 × 400 / 60 × 105 = 138.56 × 105 m3  

                              WII = V. ΔP  

                              WII = 138.56×10-5 (60-30)×105  

                                   = 4156.99 »4157 J.  

                              VIII = 2.5 × 8.314 × 400 / 30 × 105 = 277.13 × 10–5 m3  

                              WIII = 277.13×10-5 (30-1)´105  

                              WIII =8036.86 J.  

                              W total = W+ WII + WIII  

                              = 3325.6+4156.909+8036.86 = 15519.45 J.  

                     (iii) For reversible process  

                             W = 2.303 nRT log P1/P2  

                            = 2.303 × (10/4) × 8.314 × 400 × log (100/1)  

                              W = 38294.28 Jules  

Exercise:

Calculate the final volume of one mole of an ideal gas initially at 0°C and 1 atm pressure, if it absorbs 1000 cal of heat during a reversible isothermal expansion.  

Exercise:

Carbon monoxide is allowed to expand isothermally and reversibly from 10m3 to 20 m3at 300 K and work obtained is 4.754 KJ. Calculate the number of moles of carbon monoxide.    

(ii) Adiabatic Reversible Expansion of an Ideal gas:  

            q = 0  

            ΔE= -w.  

Total change in the internal energy is equal to external work done by the system.  

Work done by the system = ΔE= CvΔT.  

            and Cp-Cv = R  

On dividing all the terms by Cv.  

            Cp/Cv – Cv/Cv – R/Cv  

            Cp/Cv = γ  

            (γ – 1) = R/Cv  

            and Cv = R / (γ – 1)  

                 1014_integral.JPG  

            and = R / (γ – 1) (T2 – T1) ΔH = ΔE + PΔV.  

Thus if T2>T1, w = +ve i.e. work is done on the system.  

Thus if T21, w = -ve i.e. work is done by the system.

Related Resources
Third Law of Thermodynamics

THIRD LAW OF THERMODYNAMICS:- In all heat engines,...

Level 1 Objective Problems Of Thermodynamics

Solved Objective Examples on Thermodynamics Level...

Enthalpy of Reaction

Enthalpy of Reaction It is the enthalpy change...

Specific Heat Capacity and Its Relation with Energy

Specific Heat Capacity and Its Relation with...

Heat Capacity and Specific Heat

Specific Heat Capacity or Specific Heat [c]:- It...

Thermodynamic Process and their Types

Thermodynamic Process and their types The...

HESS Law

HESS’S LAW This law states that the amount...

Level 2 Objective Problems Of Thermodynamics

Level 2 Objective Problems of Thermodynamics Level...

Application of Bond Energies

Application of bond energies (i) Determination of...

Work done during isothermal expansion

Work Done During Isothermal Expansion:- Consider...

GIBBS Free Energy

Gibbs Free Energy This is another thermodynamic...

Application of Hess Law

Application of Hess's Law 1. Calculation of...

Relationship-Free Energy and Equilibrium Constant

Relationship between free Energy and Equilibrium...

First Law of Thermodynamics

The First Law of Thermodynamics:- The first law of...

Second Law of Thermodynamics

Second Law of Thermodynamics:- Entropy:- The...

Objective Questions of Thermodynamics

Objective Questions of Thermodynamics Prob 1 . A...

Work done during adiabatic expansion

Work Done During Adiabatic Expansion:- Consider...

Macroscopic Extensive Intensive Properties

Macroscopic Properties He properties associated...

Introduction to Thermodynamics

Introduction to Thermodynamics:- Thermodynamics:-...

Solved Problems Part 1

Solved Problems on Specific Heat, Latent Heat and...

Solved Sample Problems Based on Thermodynamics

Solved Problems on Thermodynamics:- Problem 1:- A...

State of System

State of a System When macroscopic properties of a...

Reversible Irreversible Process

Reversible and Irreversible Process:- Reversible...

Miscellaneous Exercises Part I

Miscellaneous Exercises - I Exercise 1: State,...

Bomb Calorimeter

BOMB CALORIMETER The bomb calorimeter used for...