NEET Behaviour of Perfect Gas and Kinetic Theory — Set 17

Question 1

What is the time between collisions for a gas molecule with a mean free path of $1.5 \times 10^{-7} \, \text{m}$ and average speed of 450 m/s?

Accepted Answer

$\tau = \frac{l}{ } = \frac{1.5 \times 10^{-7}}{450} = 3.33 \times 10^{-10} \, \text{s}$.

Question 2

The molar specific heat at constant pressure for a polyatomic gas with 2 vibrational modes is: ($R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}$)

Accepted Answer

Polyatomic gas: 3 translational + 3 rotational + 2 vibrational modes. Total degrees of freedom = $3 + 3 + 2 \times 2 = 10$. $C_v = 5R$, $C_p = C_v + R = 6R = 6 \times 8.31 = 49.86 \, \text{J mol}^{-1} \text{K}^{-1} $.

Question 3

A gas at 3 atm and 300 K has a volume of 10 litres. If the temperature rises to 900 K at constant pressure, what is the new volume?

Accepted Answer

Charles’ law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$. $V_1 = 10 \, \text{litres}$, $T_1 = 300 \, \text{K}$, $T_2 = 900 \, \text{K}$. $V_2 = V_1 \times \frac{T_2}{T_1} = 10 \times \frac{900}{300} = 30 \, \text{litres}$.

NEET Physics: Behaviour of Perfect Gas and Kinetic Theory — Practice Set 17

Q1. What is the time between collisions for a gas molecule with a mean free path of \(1.5 \times 10^{-7} \, \text{m}\) and average speed of 450 m/s?

Q2. The molar specific heat at constant pressure for a polyatomic gas with 2 vibrational modes is: (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q3. A gas at 3 atm and 300 K has a volume of 10 litres. If the temperature rises to 900 K at constant pressure, what is the new volume?

Q4. What is the volume of 0.3 moles of an ideal gas at 2.5 atm and 127°C? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q5. The rms speed of a gas is 350 m/s at 175 K. At what temperature will the rms speed be 700 m/s?

Q6. A gas occupies 44.8 litres at STP. How many moles are present? (Molar volume at STP = 22.4 litres)

Q7. A gas at 2 atm and 300 K occupies 20 litres. If the pressure is increased to 4 atm at constant temperature, what is the new volume?

Q8. The mean free path of a gas is \(3 \times 10^{-7} \, \text{m}\) with a number density of \(3 \times 10^{25} \, \text{m}^{-3}\). What is the molecular diameter?

Q9. A mixture of 0.4 moles of helium and 0.6 moles of nitrogen is at 400 K in a 25-litre container. What is the total pressure? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q10. A solid has a molar specific heat capacity of \(24.9 \, \text{J mol}^{-1} \text{K}^{-1}\). How many degrees of freedom per atom does it have? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))