Satish Pradhan Dnyanasadhana college, Thane

1. SatishPradhanDnyanasadhana college, Thane Subject-Physics Paper-I Class- F. Y. B. Sc Sem-I TOPIC : Behaviour of real gases Presented By Ms. Namrata A. Singh Department of Physics

2. Assumptions: • Intermolecular distances in it are so large that the attractions between • molecules are negligible and hence they move like free particles • Molecules have negligible volume • Obeys Boyle’s laws • Internal energy independent of the volume occupied Concept of a perfect gas

3. Equation of state for a perfect gas PV=nRT Where, P is pressure of a gaseous system V is volume of a gaseous system T is temperature of a gaseous system R is the universal gas constant n is number of moles of a gas

4. For a perfect gas at a fixed temperature Fig.2 (p-v isothermals for a perfect gas ) Fig.1 (p-v isothermals for a perfect gas )

5. Behaviour of real gases • At high temperatures and low pressures, gas behaves like a perfect gas • If the temperature is decreased or pressure is increased the behaviour • of a gas is very different from the behaviour of a perfect gas • At high pressure real gas does not behave as a perfect gas

6. Behaviour of real gases Behaviour of hydrogen or He Perfect gas behaviour Fig.(3) (pv-p) isothermal for hydrogen or helium) Fig.(4) (pv-p) isothermal for N2 or co2 )

7. Andrews experiment on carbon dioxide Fig.(5) Andrews apparatus to study isothermals of CO2

8. Isothermals for CO2 The curves obtained by Andrews experiment are shown in the Figure (1.5). We observe that there are two types of isothermals: (a) Above 31.1°C, the isothermals are almost rectangular hyperbola resembling the behaviour of a perfect gas. (b)  Below 31.1°C, the isothermals are not rectangular hyperbola. At 13.1°C, the portion AB of this curve shows that with the increase of pressure, volume decreases up to the point B showing gaseous behaviour of  CO2 (Boyle’s law is obeyed). From B to C, there is change of state of CO2 from gaseous to liquid (condensation) and the curve becomes parallel to the volume axis. This indicates that volume decreases without appreciable increase in pressure. After the point C, the curve is very steep indicating that after C, the substance becomes highly incompressible. At C, the gas gets liquefied completely. The portion CD represents the liquid phase of CO2. Fig.(6) Isothermals for CO2 based on Andrews experiment

9. Critical constants Definitions: 1. Critical Temperature: (TC) The temperature at which it just becomes possible to liquefy a gas under compression is known as the ‘critical temperature’. Above this temperature the gas cannot be liquefied however large the applied pressure may be. At this temperature the properties of the liquid and its saturated vapour are identical.                                                                                                                2. Critical pressure: (PC) It is the pressure necessary to liquefy a gas at critical temperature. 3. Critical Volume: (VC) It is the volume which unit mass (or one mole of a gas) of a gas occupies at the critical temperature and pressure. 4. Critical Point: It is the point on the isothermal for the critical temperature at which the change of state from gaseous to the liquid takes place under constant values of PC and VC. TC, PC and VC are collectively known as ‘critical constants’.

10. Van der Waals Equation • Modified from ideal gas equation • Accounts for: • Non-zero volumes of gas particles (repulsive effect) • Attractive forces between gas particles (attractive effect)

11. Pressure Correction • Because the molecules are attracted to each other, the pressure on the container will be less than ideal. • Pressure depends on the number of molecules per liter. • Since two molecules interact, the effect must be squared.

12. But since real gases do have volume, we need: Volume Correction • The actual volume free to move in is less because of particle size. • More molecules will have more effect. • Corrected volume V’ = V – nb • “b” is a constant that differs for each gas.

13. Van der Waal’s equation Corrected Pressure Corrected Volume • “a” and “b” are • determined by experiment • “a” and “b” are • different for each gas • bigger molecules have larger “b” • “a” depends on both • sizeandpolarity

14. Comparison of Van der Waal’s isothermals experimentals with experimental isothermals Fig.(7) Van der Waal’s isothermals

15. Critical temperature Relation between critical constants and Van der Waal’s constants Critical pressure Critical volume VC = 3b Boyle temperature(TB) .

16. Boyle Temperature Fig. (8) pv versus p isothermals

17. Brief Questions • Discuss Andrew’s experiment on carbon dioxide and explain the result using P-V diagram. • OR • Describe the Andrew's experiment with schematic diagram. • State the ideal gas equation. Discuss the Van der Waals’ corrections to the pressure and volume terms • of this equation. • OR • Derive the Van der Waals ’equation for 1 mole of a real gas. Give the SI/ cgs units of Van der Waals’ • coefficients ‘a’ and ‘b’. • Compare the Van der Waals’ isothermals with experimental isothermals for a real gas on a p-V diagram. • OR • Compare the Van der Waals’ isothermals with experimental isothermals for a real gas on a p-V diagram • Considering the Van der Waals’ equation for 1 mole of areal gas, derive the relationships between critical • constants and Van der Waals ’constants. • OR • Assuming the Van der Waals’ equation for 1 mole of a real gas, derive the following relationships • between critical constants and Van der Waals ’constants :VC = 3b, pC = a/27b2 TC = 8a/27bR. Using • this, determine the value for critical coefficient. • Describe the discrepancies between behaviour of a real gas and ideal gas with the help of isothermals • on an indicator diagram (p-V diagram) and pV V/S V diagram. • With the help of Van der Waals’ equation, derive an expression for Boyle temperature (TB = 3.375TC).

18. Define Boyle temperature and explain the behavior of real gases above and below the Boyle’s • temperature • Explain the behaviour of gases at high pressure and hence obtain the expression for Boyle’s • temperature • Comment on the limitations of the Van der Waals’ equation. • Answer in One statement: • Define the terms: Critical point • Critical temperature • Critical pressure • Critical volume • Critical coefficient • Boyle temperature. • State the ideal gas equation. • State Van der Waals’ equation of states • Give the SI/ cgs units of Van der Waals’ coefficients ‘a’ and ‘b’. • Give an expression for Boyle’s temperature

19. Fill in the blanks • The p V/S V curve at constant temperature, for a perfect gas iswith positive slope. • The pV V/S V curve at constant temperature, for a real gas is a Straight Line _________ to pV axis • The finite size of the gas molecules ______ the available volume. • Gas at high ________and low ________behaves like a perfect gas . • Real gas does not behave as a perfect gas at _______ pressure. • A perfect gas having volume of 2 m3 and initial pressure of 105 N/m2undergoes thermal expansion to a volume of 4 m3. The work done by the gas is _______ •  Certain quantity of perfect gas at NTP is compressed adiabatically to one fourth of its original volume. The resulting pressure is _______ • Certain quantity of perfect gas at NTP is compressed adiabatically to one fourth of its original volume. The resulting temperature is _______. • Certain quantity of perfect gas at NTP is compressed isothermally to one fourth of its original volume. The resulting pressure is _______. • Certain quantity of perfect gas at NTP is compressed isothermally to one fourth of its .original volume. The resulting temperature is _______ • Mayer’s relation is _______.

20. Work and Heat are path dependent but _______ is path independent • Internal energy is ______ function. • Work done by the system is ______ function. • For an ideal gas, the internal energy U is a function of ______. • The Work done by a system is considered ______ and work done on the system is considered • ______ • For a system to be in chemical equilibrium there should be no ______ within • the system. • Zeroth law of thermodynamics deal in ______. • Amount of work done in pulling the molecules a part measures the ______ • Thermodynamic process that happens slowly is known as______. • Internal energy of a perfect gas depends only upon______. • If no heat is allowed to enter or leave the system then the process is______. • The quantity that remains constant in an isothermal expansion of an ideal gas • is ______ • The dimensions of the constant ‘b’ in van der Waals equation of a state of a gas are • For an ideal gas undergoing adiabatic expansion, the temperature of the gas ______