Real gas

real gas

1. DEPARTMENT OF PHYSICS M.SC. 1 ST SEMESTER (2015-2016) SUB: STATISTICAL PHYSICS PRESENTED BY : CHITRA JAIN SUBMITTED TO : Dr H.S. SINGH

2. REAL GAS

3. REAL GAS: Real gas is one in which mutual interaction between molecules can not be neglected. i.e. Potential energy of interaction is non zero. IDEAL GAS: Ideal gas is one in which mutual interaction between molecules are negligible. i.e. Potential energy of interaction is zero.

4. PROPERTIES OF REAL GAS : 1. Real molecules do take up space & do interact with each other. 2. Real gas molecules are not point masses.so, the actual volume free to move in is less because of particle size. V ’ = V – nb “b” is a constant that differs for each gas. 3. M olecules do attract each other therefore pressure on the container will be less than ideal.

5. 4. The FUGACITY represent chemical potential for real gas. 5. Most real gas depart from ideal behaviour at deviation from - Low temperature - High Pressure 6. As in real gas Interaction between molecules is not negligible so due to interaction between molecules potential energy arises.

6. 6. As in real gas Interaction between molecules is not negligible so due to interaction between molecules potential energy arises. Acc . to plot At larger distance the atoms virtually do not interact and is zero. At smaller distance forces of mutual attraction tend to bring the atoms closer and diminishes. At a distance r is minimum. At r , repulsive force dominant and increases. = u [( ) 12 ­- 2( ) 6 ]  

7. Statistical mechanics of Ideal & Real Gas Ideal Gas Since we know that an ideal gas is one in which mutual interactions b/w molecules are negligible i.e. potential energy of interaction U=0 Hence 1. The total energy: E= K.E.+P.E. E= + U  

8. 2. The Partition Function: Partition Function for an Ideal gas: Z=[ m= mass of molecule; = Boltzmann constant; T = Temperature; h= Planck constant; V= Volume of container; N= Number of molecules;   Z=  

9. = N [ + ( ) - ] 3 . The pressure P P= P= = PV = NkT that is the equation of state of Ideal Gas.  

10. Real Gas 1. The total energy: Since we know that in case of Real gases mutual interactions can not be neglected so, The energy of a monatomic gas of N identical atoms, each of mass m is E= + U Where first term gives the K.E. of atoms & U is the sum of the potential energies of interaction b/w the pairs of atoms. U=u 12 +u 13 + ………+ u 23 +……..=  

11. 2. The Partition Function: Z = …….. this is interacting Partition Function. & so, Z= where, = …….. or = is called “ Configurational Partition Function "or “Configurational Integral” .  

12. Evaluation of : now introducing f ij = -1 …………………(1) which has the property that f ij is only appreciable when the particles are close together . in terms of this parameter the configurational integral is = f ij ) ……………….. (2) Where exponentials of the sum has been factored into product of exponentials. Expansion of product is as follows f ij )=1+ + +…(3 )  

13. With this expansion it is possible to find terms of different order., in terms of number of particles that are involved. The 1 st term is single particle term, the 2 nd term corresponds to the two particle interaction, the 3 rd to the three particle interaction & so on. Such expansion is called the CLUSTER EXPANSION(Series expansion to handle inter-particle interactions) E ach term represent the interaction within clusters of a certain number of particles. Contribution to third term may be represented as i,j,k,l,distict i =k i =k & j=l

14. Substituting the ( 3 ) in (2) expansion of + +………….( 4) now substituting the for free energy eq. of state of real gas PV= NKT (1+ (T) + (T) +…… known as “virial equation” and components (T) are the “virial coefficients.  

15. Hence, where b’= and a’= Hence, = n + (neglecting higher terms ) n= where is Avogadro number and v is molar volume.  

16. (V- = K where a= a’N A ; b= b’N A ; R= N A K   The correction term ‘a’ comes from the long range weak attractive force b/w molecules. ‘b’ comes from volume of the molecule.

17. THANK YOU