Question 1

If the temperature of an ideal gas is increased from 300 K to 600 K while volume remains constant, by what factor does the pressure increase?

Accepted Answer

At constant volume, pressure is directly proportional to absolute temperature (Gay-Lussac's Law), so P₂/P₁ = T₂/T₁ = 600/300 = 2.

Question 2

A gas has 2 × 10²³ molecules at 400 K. If the Boltzmann constant k = 1.38 × 10⁻²³ J/K, what is the total average kinetic energy of all molecules?

Accepted Answer

Total kinetic energy = N × (3/2)kT = 2×10²³ × 1.5 × 1.38×10⁻²³ × 400 = 2 × 1.5 × 1.38 × 400 = 4140 J.

Question 3

At the same temperature, which gas will have the highest average kinetic energy per molecule?

Accepted Answer

Average kinetic energy per molecule depends only on temperature (KE_avg = 3kT/2), not on the type or mass of gas.

Question 4

The root mean square speed of gas molecules depends on which of the following factors?

Accepted Answer

RMS speed is given by v_rms = √(3RT/M) or √(3kT/m), which depends only on absolute temperature and molar mass.

Question 5

According to kinetic theory, the average kinetic energy of a gas molecule at temperature T is directly proportional to which quantity?

Accepted Answer

The average kinetic energy of gas molecules is given by (3/2)kT, which is directly proportional to absolute temperature T.

Question 6

At what temperature will the average kinetic energy of a gas molecule equal 6.21 × 10⁻²¹ J? (Use k_B = 1.38 × 10⁻²³ J/K)

Accepted Answer

From KE_avg = (3/2)k_B·T, we get T = (2 × 6.21 × 10⁻²¹)/(3 × 1.38 × 10⁻²³) = 150 K.

Question 7

The mean free path λ of gas molecules is inversely proportional to which factors according to kinetic theory?

Accepted Answer

Mean free path is given by λ = 1/(√2·π·d²·n), so it is inversely proportional to both n and d².

Question 8

A container holds nitrogen gas (N₂) at 300 K with RMS velocity 500 m/s. If the same gas is heated to 1200 K, what will be the new RMS velocity?

Accepted Answer

Since v_rms ∝ √T, the new velocity = 500 × √(1200/300) = 500 × √4 = 500 × 2 = 1000 m/s.

Question 9

Which of the following statements about kinetic theory is CORRECT?

Accepted Answer

Kinetic theory assumes gas molecules occupy negligible volume; all other statements contradict its basic assumptions.

Question 10

The pressure of an ideal gas according to kinetic theory is expressed as P = (1/3)ρ·v_rms². If the density ρ of the gas is doubled while keeping v_rms constant, the pressure will:

Accepted Answer

Since P ∝ ρ when v_rms is constant, doubling ρ will double the pressure.

Question 11

According to kinetic theory, the average kinetic energy of a gas molecule at temperature T is directly proportional to which of the following?

Accepted Answer

The average kinetic energy of a gas molecule is given by KE_avg = (3/2)k_B·T, which is directly proportional to absolute temperature.

Question 12

A gas has 2 × 10²³ molecules in a container of volume 2 L at temperature 300 K. What is the number density (molecules per unit volume) of the gas?

Accepted Answer

Number density n = N/V = (2 × 10²³)/(2 × 10⁻³ m³) = 1 × 10²⁹ m⁻³.

Question 13

The root mean square (RMS) velocity of gas molecules is given by v_rms = √(3k_B·T/m). If the temperature of a gas is increased 4 times, by what factor does the RMS velocity increase?

Accepted Answer

Since v_rms ∝ √T, when T increases by 4 times, v_rms increases by √4 = 2 times.

Question 14

According to kinetic theory, pressure exerted by a gas is due to which of the following?

Accepted Answer

Kinetic theory states that gas pressure arises from elastic collisions of rapidly moving molecules with the container walls.

Question 15

Two gases A and B have molecular masses in ratio M_A : M_B = 1 : 4. If both gases are at the same temperature and pressure, what is the ratio of their RMS speeds v_A : v_B?

Accepted Answer

RMS speed v = √(3RT/M); v_A/v_B = √(M_B/M_A) = √(4/1) = 2, so v_A : v_B = 2 : 1.

Question 16

A gas has molecular mass M = 32 g/mol at temperature T = 300 K. If the average kinetic energy per molecule is 6.21 × 10⁻²¹ J, what is the number of translational degrees of freedom? (k_B = 1.38 × 10⁻²³ J/K)

Accepted Answer

From KE_avg = (f/2)k_B T, solving f = (2 × 6.21 × 10⁻²¹)/(1.38 × 10⁻²³ × 300) = 3, representing translational motion in three dimensions.

Question 17

The root mean square speed of oxygen molecules at 27°C is 450 m/s. What will be the RMS speed at 327°C? (Assume oxygen behaves as an ideal gas)

Accepted Answer

RMS speed is proportional to √T; v₂/v₁ = √(T₂/T₁) = √(600/300) = √2, so v₂ = 450√2 ≈ 636 m/s (closest is 600 m/s); correction: √(600/300) = √2 gives 637 m/s, but 900 is incorrect unless recalculated: actually answer is 450√2 ≈ 636, closest option is 600 m/s (B), but checking: 327°C=600K, 27°C=300K, ratio=2, so speed increases by √2 ≈1.414, giving 637 m/s—reviewing: 900 m/s would require T ratio of 4.

Question 18

At what temperature will the average kinetic energy of gas molecules be equal to 1 eV? (Given: Boltzmann constant k_B = 1.38 × 10⁻²³ J/K, 1 eV = 1.6 × 10⁻¹⁹ J)

Accepted Answer

From KE_avg = (3/2)k_B T, solving T = (2 × 1.6 × 10⁻¹⁹)/(3 × 1.38 × 10⁻²³) ≈ 11620 K.

Agniveer Army Technical Kinetic Theory

Kinetic Theory — Practice Questions