Kinetic Theory Assumptions and Derivation - UNSOLVED PRACTICE SET
Chapter: Kinetic Theory of Gases | Topic: Kinetic Theory Assumptions and Derivation
KINETIC THEORY ASSUMPTIONS AND DERIVATION - UNSOLVED PRACTICE SET
Topic: Kinetic Theory Assumptions and Derivation
Multiple Choice Questions
Q1. According to kinetic theory, the molecules of an ideal gas:
- Are at rest
- Move in straight lines with constant velocity between collisions
- Attract each other strongly
- Have finite size comparable to the container
Q2. The time of collision between molecules is assumed to be:
- Very large
- Very small compared to time between collisions
- Equal to time between collisions
- Infinite
Q3. In kinetic theory, collisions between molecules and with walls are assumed to be:
- Inelastic
- Perfectly elastic
- Partially elastic
- Absent
Q4. The kinetic theory assumes that the number of molecules in a gas is:
- Very small
- Very large
- Exactly 6.022 × 10²³
- Equal to Avogadro's number only
Q5. The average kinetic energy of gas molecules is assumed to be proportional to:
- Pressure
- Volume
- Absolute temperature
- Number of moles
Q6. When you inflate a bicycle tire using a hand pump, the pump becomes warm. Kinetic theory explains this because:
- Heat flows from the pump to the gas
- Work done on the gas increases the kinetic energy of molecules
- The pump is made of metal
- Air molecules stick to the pump walls
Short Answer Questions
Q7. List any four assumptions of the kinetic theory of gases.
Q8. Why does kinetic theory assume that intermolecular forces are negligible for an ideal gas? What would happen if this assumption were not true?
Q9. Explain why kinetic theory assumes that the volume of molecules is negligible compared to the volume of the container.
Q10. What is meant by the mean free path of a molecule? How is it related to the assumptions of kinetic theory?
Q11. Why is kinetic theory not applicable to solids and liquids in the same way as to gases?
Q12. Explain how the assumption of perfectly elastic collisions leads to the conclusion that there is no net loss of kinetic energy in the gas.
Long Answer Questions
Q13. State all the postulates of the kinetic theory of gases. For each postulate, explain:
(i) Why it is necessary for the derivation
(ii) In what situations real gases deviate from this assumption
(iii) How the theory would change if this assumption were removed
Q14. Derive the expression for pressure exerted by an ideal gas on the walls of its container using kinetic theory. Start from the basic assumptions and show all steps clearly:
Consider a molecule moving with velocity v_x in a cubical container of side L
Calculate the change in momentum per collision
Calculate the number of collisions per unit time
Find the force and pressure
Extend to all molecules and show that P = (1/3)nmv²_rms
Q15. Using kinetic theory, derive the relation between pressure and kinetic energy of gas molecules: P = (2/3)(E/V), where E is the total translational kinetic energy and V is the volume. Explain the physical significance of this result.
Numerical / Application-Based Problems
Q16. A cubical container of side 10 cm contains 10²⁴ molecules of an ideal gas. Each molecule has a mass of 5 × 10⁻²⁶ kg and an rms speed of 500 m/s.
(i) Calculate the total kinetic energy of all the molecules.
(ii) Calculate the pressure exerted on the walls of the container.
(iii) If the temperature of the gas is 300 K, verify that the average kinetic energy per molecule is (3/2)kT.
(iv) If the number of molecules is doubled while keeping temperature constant, what happens to the pressure?
(Given: k = 1.38 × 10⁻²³ J/K)
Q17. In a school laboratory, a cubical box of side 20 cm contains nitrogen gas at 300 K. The mass of a nitrogen molecule is 4.65 × 10⁻²⁶ kg. The rms speed of nitrogen molecules at 300 K is 515 m/s.
(i) Calculate the change in momentum when one molecule collides elastically with a wall perpendicular to the x-axis.
(ii) Calculate the time between successive collisions of this molecule with the same wall.
(iii) Calculate the average force exerted by this one molecule on the wall.
(iv) If there are 3 × 10²² molecules in the box, calculate the total pressure on the wall.
Q18. A container of volume 2 × 10⁻³ m³ contains 5 × 10²² molecules of oxygen gas at 300 K.
(i) Calculate the number density of the gas.
(ii) Using kinetic theory, calculate the pressure of the gas if the rms speed of oxygen molecules is 480 m/s. (Mass of O₂ molecule = 5.32 × 10⁻²⁶ kg)
(iii) Verify your answer using the ideal gas equation.
(iv) If the temperature is doubled, by what factor does the pressure change? Explain using both kinetic theory and the ideal gas equation.