Prepared by Dr. A. Mekki

 
Summary of chapter 20

                                                                                                           

                       

  1. The number of moles, n, in a substance is

 

where N is the number of molecules, m is the mass of the substance, M is the molar mass of the substance and NA is Avogadros number.

 

NA = 6.02 x 10-23 molecules/mole (is the number of molecules in ONE mole of the substance).

 

  1. All real gases behave as ideal gases at low pressure. The relationship between the temperature T, the volume V, and the pressure P in this case is

            The ideal gas law

 

R = 8.31 J/mole K, is the gas constant and n is the number of moles of the gas.

 

     We have three situations

     (i) Temperature constant (isothermal process)               

     (ii) Volume constant (isochoric process)                        

     (iii) Pressure constant (isobaric process)                        

     In the above equations T in Kelvin.

 

 

  1. For an isothermal process, the work done on or by the gas is

 

              T in Kelvin

     For an isobaric process, the work done on or by the gas is

 

W = P DV

 

If Vf > Vi (expansion), then W > 0, the gas do work

 

If Vf < Vi (compression), then W < 0, external work is done on the gas.

 

  1. The pressure of N molecules of an ideal gas is given by;

 

 

   where vrms is the root-mean-square speed of the gas molecules =

 

          This speed is related to the molar mass and the temperature of the gas as

          follows:

        T in Kelvin

         

         

  1. The average translational kinetic energy of an ideal gas containing N molecules is related to the temperature of the gas by

 

          T in Kelvin

 

          k = 1.38 x 10-23 J/K is Boltzman constant.

         

         

  1. The internal energy of a monoatomic ideal gas is

 

           T in Kelvin

 

          Therefore the change in internal energy is

 

So: for an isothermal process the change in internal energy of the gas is ZERO because DT = 0.

 

  1.  The heat absorbed or expelled by a gas depends on the process.

 

 

(i)                for a constant volume process (isochoric) the heat is given by

 

 

 

(ii)              for a constant pressure process (isobaric) the heat is given by

 

             

  1. For an adiabatic process (Q = 0), the macroscopic thermodynamic variables (P, V, T) are related by

 

 

             T in Kelvin

 

where  is the specific heat ratio (constant).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary

 

Process

 

P-V diagram

 

W

 

Q

 

DEint

 

Isothermal

 

0

 

Isobaric

 

P DV

 

n Cp DT

 

n Cv DT

 

Isochoric

 

0

 

n Cv DT

 

n Cv DT

 

Adiabatic

 

- n Cv DT

 

0

 

n Cv DT

 

Cyclic

 

Area enclosed

 

Area enclosed

 

0

 

 

Note:              This is ALWAYS true, for all processes!

 

 

Gas

Cv

Cp

g = Cp/Cv

Monoatomic

3/2 R

5/2 R

1.67

Diatomic

5/2 R

7/2 R

1.4

 

Cp = Cv + R