Grade 11 Physics: Kinetic Theory Practice Quiz (Set 2)

Question 1

An ideal gas sample containing 2 moles occupies a volume of $0.0831 m^3$ at a temperature of 300 K. What is the pressure exerted by the gas? (Take $R = 8.31 ext{ J/(mol}\cdot ext{K)}$).

Accepted Answer

B) $6 	imes 10^4	ext{ Pa}$

Answer

A) $3 	imes 10^4	ext{ Pa}$

Answer

C) $1.2 	imes 10^5	ext{ Pa}$

Answer

D) $8.31 	imes 10^4	ext{ Pa}$

Question 2

If the absolute temperature of a monoatomic ideal gas is quadrupled (increased by a factor of 4), by what factor does the root mean square speed ($v_{rms}$) of its molecules increase?

Accepted Answer

A) 2 times

Answer

B) 4 times

Answer

C) 8 times

Answer

D) 16 times

Question 3

The average translational kinetic energy of a single molecule of an ideal gas is directly proportional to which physical quantity?

Accepted Answer

C) Absolute temperature of the gas

Answer

A) Volume of the gas

Answer

B) Pressure of the gas

Answer

D) Molar mass of the gas

Question 4

How many total degrees of freedom does a rigid diatomic gas molecule (such as $ ext{N}_2$ or $ ext{O}_2$) possess at room temperature?

Accepted Answer

B) 5

Answer

A) 3

Answer

C) 6

Answer

D) 7

Question 5

According to the Law of Equipartition of Energy, what is the average thermal energy associated with EACH degree of freedom per molecule of gas at temperature $T$?

Accepted Answer

B) $\frac{1}{2} k_B T$

Answer

A) $k_B T$

Answer

C) $\frac{3}{2} k_B T$

Answer

D) $\frac{5}{2} k_B T$

Question 6

What is the theoretical ratio of specific heat capacities $\gamma = \frac{C_p}{C_v}$ for an ideal monoatomic gas?

Accepted Answer

C) 1.67

Answer

A) 1.33

Answer

B) 1.40

Answer

D) 1.50

Question 7

A rigid container holds 1 mole of Helium gas at a partial pressure of 20 kPa and 3 moles of Argon gas at the same temperature. What is the total pressure of the gas mixture inside the container?

Accepted Answer

C) 80 kPa

Answer

A) 40 kPa

Answer

B) 60 kPa

Answer

D) 100 kPa

Question 8

How does the mean free path ($\lambda$) of gas molecules depend on the molecular diameter $d$?

Accepted Answer

C) Inversely proportional to $d^2$

Answer

A) Directly proportional to $d$

Answer

B) Inversely proportional to $d$

Answer

D) Independent of $d$

Question 9

What is the total internal energy ($U$) of $n$ moles of an ideal monoatomic gas at absolute temperature $T$?

Accepted Answer

B) $\frac{3}{2} nRT$

Answer

A) $\frac{1}{2} nRT$

Answer

C) $\frac{5}{2} nRT$

Answer

D) $3 nRT$

Question 10

Which of the following is a fundamental assumption of the Kinetic Theory of Ideal Gases?

Accepted Answer

B) Intermolecular forces of attraction are negligible except during collisions

Answer

A) Molecules attract each other strongly at standard distance

Answer

C) Collisions between gas molecules are inelastic

Answer

D) The total volume occupied by gas molecules is significant relative to container volume

Question 11

Oxygen gas ($O_2$, molar mass $= 32 ext{ g/mol}$) and Hydrogen gas ($H_2$, molar mass $= 2 ext{ g/mol}$) are at the same temperature. What is the ratio of the RMS speed of Hydrogen molecules to Oxygen molecules ($v_{H2} : v_{O2}$)?

Accepted Answer

C) 4 : 1

Answer

A) 1 : 4

Answer

B) 2 : 1

Answer

D) 16 : 1

Question 12

According to kinetic theory, what is the relation between pressure $P$, gas density $\rho$, and root mean square speed $v_{rms}$?

Accepted Answer

A) $P = \frac{1}{3} \rho v_{rms}^2$

Answer

B) $P = \frac{1}{2} \rho v_{rms}^2$

Answer

C) $P = \rho v_{rms}^2$

Answer

D) $P = \frac{3}{2} \rho v_{rms}^2$

Question 13

For an ideal gas at temperature $T$, which option correctly arranges the most probable speed ($v_{mp}$), average speed ($v_{avg}$), and root mean square speed ($v_{rms}$) in increasing order?

Accepted Answer

B) $v_{mp} < v_{avg} < v_{rms}$

Answer

A) $v_{rms} < v_{avg} < v_{mp}$

Answer

C) $v_{avg} < v_{mp} < v_{rms}$

Answer

D) $v_{mp} < v_{rms} < v_{avg}$

Question 14

If the pressure of an ideal gas is doubled while holding temperature constant, what happens to its mean free path ($\lambda$)?

Accepted Answer

B) Halves

Answer

A) Doubles

Answer

C) Quadruples

Answer

D) Remains unchanged

Question 15

A non-rigid diatomic gas has 5 translational and rotational degrees of freedom, plus 1 active vibrational mode (contributing 2 degrees of freedom). What is its molar heat capacity at constant volume ($C_v$)?

Accepted Answer

C) $\frac{7}{2} R$

Answer

A) $\frac{3}{2} R$

Answer

B) $\frac{5}{2} R$

Answer

D) $4 R$

Question 16

The Boltzmann constant $k_B$ is defined mathematically as the ratio of which two physical constants?

Accepted Answer

A) Universal gas constant ($R$) to Avogadro's number ($N_A$)

Answer

B) Planck's constant to speed of light

Answer

C) Stefan's constant to gas constant

Answer

D) Mass of electron to mass of proton

Question 17

In the Maxwell-Boltzmann distribution graph plotting fraction of molecules versus speed, what physical quantity corresponds to the peak of the curve?

Accepted Answer

C) Most probable speed

Answer

A) Root mean square speed

Answer

B) Average speed

Answer

D) Speed of sound in the gas

Question 18

According to Avogadro's Law, equal volumes of all ideal gases under identical conditions of temperature and pressure contain equal numbers of:

Accepted Answer

B) Molecules

Answer

A) Atoms

Answer

C) Electrons

Answer

D) Protons

Question 19

Based on kinetic interpretation of temperature, what happens to the pressure of an ideal gas as its absolute temperature approaches absolute zero (0 K)?

Accepted Answer

B) Pressure drops to zero because translational molecular motion ceases

Answer

A) Pressure approaches infinity

Answer

C) Pressure remains constant

Answer

D) Pressure fluctuates endlessly

Question 20

For a fixed amount of an ideal gas, its internal energy depends strictly on which thermodynamic parameter?

Accepted Answer

C) Absolute temperature only

Answer

A) Volume only

Answer

B) Pressure only

Answer

D) Density only

Set 2Grade 11 : Physics - Kinetic Theory