NEET Behaviour of Perfect Gas and Kinetic Theory — Set 7

Question 1

The rms speed of a gas is 300 m/s at 150 K. At what temperature will the rms speed be 600 m/s?

Accepted Answer

$v_{\text{rms}} \propto \sqrt{T}$, $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$. $\frac{600}{300} = \sqrt{\frac{T_2}{150}}$, $2 = \sqrt{\frac{T_2}{150}}$. Square both sides: $4 = \frac{T_2}{150}$, $T_2 = 600 \, \text{K}$.

Question 2

A gas at 2 atm and 400 K has a volume of 6 litres. If the pressure decreases to 1 atm at constant temperature, what is the new volume?

Accepted Answer

Boyle’s law: $P_1 V_1 = P_2 V_2$. $P_1 = 2 \, \text{atm}$, $V_1 = 6 \, \text{litres}$, $P_2 = 1 \, \text{atm}$. $V_2 = \frac{P_1 V_1}{P_2} = \frac{2 \times 6}{1} = 12 \, \text{litres}$.

Question 3

What is the total internal energy of 0.3 moles of a triatomic gas at 300 K with no vibrational modes? ($R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}$)

Accepted Answer

Triatomic gas: 6 degrees of freedom, $U = 3 \mu R T$. $U = 3 \times 0.3 \times 8.31 \times 300 = 2243.7 \, \text{J} \approx 2.24 \, \text{kJ}$.

NEET Physics: Behaviour of Perfect Gas and Kinetic Theory — Practice Set 7

Q1. The rms speed of a gas is 300 m/s at 150 K. At what temperature will the rms speed be 600 m/s?

Q2. A gas at 2 atm and 400 K has a volume of 6 litres. If the pressure decreases to 1 atm at constant temperature, what is the new volume?

Q3. What is the total internal energy of 0.3 moles of a triatomic gas at 300 K with no vibrational modes? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q4. The mean free path of a gas is \(5 \times 10^{-7} \, \text{m}\) with a number density of \(2 \times 10^{25} \, \text{m}^{-3}\). What is the molecular diameter?

Q5. A gas mixture contains 4 g of helium and 16 g of oxygen. What is the ratio of their partial pressures?

Q6. What is the average translational kinetic energy of an argon atom at 500 K? (\(k_B = 1.38 \times 10^{-23} \, \text{J K}^{-1}\))

Q7. How much heat is required to raise the temperature of 0.1 moles of a monatomic gas by 30 K at constant volume? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q8. A mixture of 2 moles of helium and 3 moles of nitrogen is at 400 K in a 50-litre container. What is the total pressure? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q9. A gas at 4 atm and 500 K has a volume of 20 litres. If the pressure increases to 8 atm at constant temperature, what is the new volume?

Q10. What is the ratio of \(C_p\) to \(C_v\) for a gas with 3 translational and 2 rotational degrees of freedom?