NEET Behaviour of Perfect Gas and Kinetic Theory — Set 16

Question 1

A solid has a molar specific heat capacity of $24.4 \, \text{J mol}^{-1} \text{K}^{-1}$. How many degrees of freedom per atom does it have? ($R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}$)

Accepted Answer

$C = f \times \frac{R}{2}$, $24.4 = f \times \frac{8.31}{2}$. $f = \frac{24.4 \times 2}{8.31} \approx 5.87 \approx 6$.

Question 2

What is the average translational kinetic energy of an argon atom at 900 K? ($k_B = 1.38 \times 10^{-23} \, \text{J K}^{-1}$)

Accepted Answer

Average translational KE = $\frac{3}{2} k_B T$. $\frac{3}{2} \times 1.38 \times 10^{-23} \times 900 = 1.863 \times 10^{-20} \, \text{J}$.

Question 3

What is the collision frequency of a gas molecule with a mean free path of $2.4 \times 10^{-7} \, \text{m}$ and average speed of 480 m/s?

Accepted Answer

Collision frequency = $\frac{ }{l}$. $\frac{480}{2.4 \times 10^{-7}} = 2.0 \times 10^9 \, \text{s}^{-1}$.

NEET Physics: Behaviour of Perfect Gas and Kinetic Theory — Practice Set 16

Q1. A solid has a molar specific heat capacity of \(24.4 \, \text{J mol}^{-1} \text{K}^{-1}\). How many degrees of freedom per atom does it have? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q2. What is the average translational kinetic energy of an argon atom at 900 K? (\(k_B = 1.38 \times 10^{-23} \, \text{J K}^{-1}\))

Q3. What is the collision frequency of a gas molecule with a mean free path of \(2.4 \times 10^{-7} \, \text{m}\) and average speed of 480 m/s?

Q4. A gas has a \(C_v\) of \(24.93 \, \text{J mol}^{-1} \text{K}^{-1}\). What is the ratio of specific heats (\(\gamma\))? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q5. A gas mixture has equal numbers of helium and nitrogen molecules at 400 K. What is the ratio of their rms speeds? (Atomic mass: He = 4 u, \(N_2 = 28 \, \text{u}\))

Q6. At what temperature is the rms speed of neon molecules 620 m/s? (Atomic mass of Ne = 20.2 u, \(k_B = 1.38 \times 10^{-23} \, \text{J K}^{-1}\))

Q7. What is the total internal energy of 0.5 moles of a diatomic gas at 200 K with no vibrational modes? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q8. What is the average speed of a molecule if its mean free path is \(4 \times 10^{-7} \, \text{m}\) and time between collisions is \(8 \times 10^{-10} \, \text{s}\)?

Q9. A gas at 2 atm and 400 K has a density of \(0.8 \, \text{kg m}^{-3}\). What is its molecular mass? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\), 1 atm = \(1.01 \times 10^5 \, \text{Pa}\))

Q10. The ratio of specific heats (\(\gamma\)) for a triatomic gas with no vibrational modes is: