Kinetic Theory of Gases — Previous-Year Questions

Q1. Brownian motion provides evidence for:

Q2. Average velocity of gas molecules in a container at rest:

Q3. Graham's law of effusion: rate ∝

Q4. Random walk: after time t, mean displacement scales as:

Q5. If you double T (same gas), average molecular speed increases by factor:

Q1. When a molecule of mass m and velocity v hits wall perpendicularly and bounces back elastically, the momentum change is:

Q2. If number density n is doubled (same v_rms), pressure:

Q3. Pressure of an ideal gas at constant V depends on:

Q4. When a molecule's v_rms doubles, pressure (at constant n, m):

Q5. Pressure of a gas is caused primarily by:

Q1. Kinetic theory pressure formula P = (1/3)·ρ·v_rms². If T doubles, P doubles because:

Q2. v_rms of N₂ at 300 K (M = 28 g/mol):

Q3. Mean KE per molecule of an ideal gas at temperature T:

Q4. Kinetic-theory pressure derivation assumes:

Q5. If number of molecules doubles (same T), pressure (at constant V):

Q1. v_rms of H₂ (M = 2 g/mol) at 300 K:

Q2. Ratio of v_rms of H₂ vs O₂ at same T:

Q3. If T quadruples, v_rms:

Q4. Most probable speed vs RMS speed (same gas, same T):

Q5. If two gases have same v_rms, then:

Q1. If temperature is doubled, mean KE per molecule:

Q2. Mean KE per mole of monatomic ideal gas at 300 K:

Q3. Two ideal gases (H₂ and O₂) at SAME T have:

Q4. Equipartition theorem: each DoF gets:

Q5. At T = 0 K classically:

Q1. Maxwell distribution peaks at speed:

Q2. If T doubles, Maxwell distribution:

Q3. Why do light atmospheric gases (H, He) escape Earth's atmosphere?

Q4. Three Maxwell speeds in order (low to high):

Q5. Maxwell distribution applies to:

Q1. Gas at 1 atm and 2 L is compressed to 0.5 L (constant T). New pressure:

Q2. Boyle's law holds at:

Q3. On PV diagram, Boyle's law gives:

Q4. Air in a 1 L sealed syringe (1 atm) compressed to 0.25 L. Pressure rises to:

Q5. Why does ear popping occur when ascending in altitude?

Q1. Gas at 300 K, V = 2 L. At constant P, V at 600 K:

Q2. Charles's law uses temperature in:

Q3. If V is plotted against T (Celsius), graph is:

Q4. Volume of a gas at constant P doubles when T (K) is:

Q5. Hot air balloons work because:

Q1. Sealed gas at 1 atm and 300 K. Heated to 600 K. New pressure (constant V):

Q2. Why do aerosol cans say 'do not heat'?

Q3. If T (K) is tripled at constant V, pressure becomes:

Q4. On P vs T (Kelvin) graph at constant V:

Q5. A pressure cooker cooks faster because:

Q1. Mean free path of air molecules at 1 atm and 25°C is approximately:

Q2. If number density n is halved (same T), mean free path:

Q3. Mean free path vs altitude (Earth's atmosphere):

Q4. If molecular diameter d is doubled (same n), λ:

Q5. Collision frequency at sea level for air:

Q1. Degrees of freedom of a diatomic ideal gas at room temperature:

Q2. γ for monatomic gas:

Q3. Diatomic gas at very high T (vibrations active):

Q4. Specific heat at constant V for monatomic gas:

Q5. Energy associated with each DoF per molecule: