Kinetic theory of gases

This assignment contains all important questions of the chapter kinetic theory of gases

KINETIC THEORY OF GASES

1. What are the basic assumptions of kinetic theory of gases ? on their basis, derive an expression for the pressure exerted by an ideal gas.
2. What is meant by degrees of freedom? State the law of equipartition of energy. Hence calculate the values of molar specific heats at constant volume and pressure for monoatomic , diatomic and triatomic gases.
3. Calculate the kinetic energy of one mole of argon at 127⁰ given that N =6.02×10²³ mol and k=1.381 x10^-23 mol^-1K^-1
4. Calculate the number of degrees of freedom for one mole of diatomic gas at N.T.P
5. Calculate the number of degrees of freedom of 1 cm³ of helium gas at N.T.P.
6. A vessel contains argon gas at 127⁰ find the average kinetic energy of argon molecule, if Boltzmann’s constant, k=1.38 x 10^-23 j mol ^-1 K^-1
7. Calculate the total kinetic energy of 1g of helium at 27⁰C Given that R =8.31 mole ^-1 K^-1.
8. At what temperature is the r.m.s velocity of a hydrogen molecule equal to that of a oxygen molecule at 47⁰C ?
9. Give the kinetic interpretation of temperature and define absolute temperature.

• 10. If three molecules have velocities 0.5,1 and 2km s^-1 respectively, calculate the relation between the root mean square speed and average speed.
• 11. Calculate the temperature at which the r.m.s velocity of a hydrogen will be equal to 8km/hr. given that R =8.31 j mole ^-1.
• 12.Calculate the r.m.s velocity of CO₂ molecules at N.T.P. given, R=8.31 j mol ^-1 K^-1 .
• 13. Calculate the r.m.s velocity of hydrogen at N.T.P. given that density of the gas is 9×10^-5 g cm ^-3.
• 14. Find the temperature at which the root mean square velocity of a gas is double than that its value at 0 ⁰C , pressure remaining constant.
• 15. The molar gas volume at S.T.P. is 22.4 litre and Avogadro number is 6.023×10²³. (a) calculate the number of gas molecules per unit volume,
• 16. Draw a graph to show the variation of V² _rms with absolute temperature .
• 17. When an ideal gas undergoes an isothermal expansion, the pressure of the gas in the encloser falls. Why?
• 18. Two identical cylinders contains helium at 2.5 atmosphere and organ at 1 atmosphere. Find pressure if both the gases are filled in one of the cylinders?
• 19. The temperature of argon, kept in vessel, is raised by 1⁰C at constant volume. The total heat supplied to the gas is a combination of translational energies. Find their respective shares.
• 20. A gas mixture consist of 2 moles of oxygen and 4 moles of argon at temperature T. find total internal energy of the system, when vibrational modes are rejected.