Behaviour of Gases Gas Laws - UNSOLVED PRACTICE SET
Chapter: Kinetic Theory of Gases | Topic: Behaviour of Gases Gas Laws
BEHAVIOUR OF GASES GAS LAWS - UNSOLVED PRACTICE SET
Topic: Behaviour of Gases Gas Laws
Multiple Choice Questions
Q1. Boyle's law states that for a fixed mass of gas at constant temperature:
- P ∝ V
- P ∝ 1/V
- P ∝ T
- V ∝ T
Q2. A balloon is taken from a warm room to a cold refrigerator. Assuming pressure remains constant, the volume of the balloon will:
- Increase
- Decrease
- Remain the same
- Become zero
Q3. At constant volume, the pressure of a gas is directly proportional to its absolute temperature. This is known as:
- Boyle's law
- Charles's law
- Gay-Lussac's law
- Avogadro's law
Q4. A gas at 27°C is heated to 127°C at constant pressure. The ratio of final volume to initial volume is:
- 27/127
- 127/27
- 400/300
- 300/400
Q5. The graph of pressure versus volume for a gas at constant temperature is a:
- Straight line
- Parabola
- Hyperbola
- Circle
Q6. On a hot summer day in Delhi, a truck tire is inflated to a certain pressure in the morning. By afternoon, the tire feels much harder. This is because:
- The air inside has increased in mass
- The pressure has increased due to temperature rise
- The volume of the tire has decreased
- The rubber has expanded
Short Answer Questions
Q7. State Boyle's law and Charles's law. Write the mathematical expressions for each.
Q8. What is an ideal gas? Why do real gases deviate from ideal gas behaviour at high pressure and low temperature?
Q9. Draw P-V diagrams for:
(i) An isothermal process (Boyle's law)
(ii) An isobaric process (Charles's law)
Label the axes and indicate the direction of change.
Q10. Explain why the pressure of a gas in a sealed container increases when heated, using the molecular picture.
Q11. A pressure cooker whistle releases steam when the pressure inside exceeds a certain value. Explain this using Gay-Lussac's law.
Q12. What is absolute zero? Why is it called "absolute" zero? What happens to the volume of an ideal gas at absolute zero according to Charles's law?
Long Answer Questions
Q13. Derive the combined gas law from Boyle's law, Charles's law, and Gay-Lussac's law. Starting from the three individual laws, show step by step how PV/T = constant for a fixed mass of gas. Explain the conditions under which each law is valid.
Q14. Discuss the behaviour of real gases and how they deviate from ideal gas behaviour. Explain the role of:
(i) Finite size of molecules
(ii) Intermolecular forces
Draw a graph showing the deviation of real gases from ideal gas behaviour (compressibility factor Z vs P) and explain the significance of Z = 1, Z > 1, and Z < 1.
Q15. A student conducts an experiment with a bicycle pump. She compresses the air inside the pump slowly, keeping the temperature constant.
(i) Which gas law is being demonstrated?
(ii) If the initial volume is 200 cm³ at 1 atm, and the final volume is 50 cm³, what is the final pressure?
(iii) If she now heats the compressed air at constant volume until the pressure returns to 1 atm, what is the final temperature? (Assume initial temperature was 27°C)
(iv) Draw the P-V diagram showing both processes.
Numerical / Application-Based Problems
Q16. A gas occupies 2.0 L at 300 K and 1.0 × 10⁵ Pa. It is first heated at constant pressure to 400 K, then compressed isothermally back to 2.0 L.
(i) Calculate the volume after the heating process.
(ii) Calculate the pressure after the isothermal compression.
(iii) Calculate the total work done in the two processes.
(iv) Draw a P-V diagram showing both processes with proper labels.
Q17. An oxygen cylinder used in a hospital has a volume of 50 L and contains oxygen at 150 atm pressure and 27°C.
(i) Calculate the number of moles of oxygen in the cylinder.
(ii) If the oxygen is allowed to expand isothermally to 1 atm, what volume would it occupy?
(iii) If instead, the temperature is raised to 57°C at constant volume, what is the new pressure?
(iv) Which of these two scenarios is more dangerous? Explain why.
(Given: R = 8.31 J mol⁻¹ K⁻¹)
Q18. A hot air balloon has a volume of 2000 m³ at 27°C and 1 atm. The air inside is heated to 87°C while the pressure remains constant (equal to atmospheric pressure).
(i) Calculate the new volume of the hot air inside the balloon.
(ii) Calculate the mass of air that escapes from the balloon. (Density of air at 27°C = 1.2 kg/m³)
(iii) Explain why the balloon rises after heating. Use the concept of buoyancy and gas laws.
(iv) If the maximum safe volume of the balloon is 2500 m³, what is the maximum temperature to which the air can be heated?