NEET Behaviour of Perfect Gas and Kinetic Theory — Set 15

Question 1

A mixture of 1 mole of argon and 0.5 moles of nitrogen is at 450 K in a 15-litre container. What is the total pressure? ($R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}$)

Accepted Answer

$PV = \mu R T$, $P = \frac{\mu R T}{V}$. Total moles = $1 + 0.5 = 1.5$, $V = 15 \times 10^{-3} \, \text{m}^3$. $P = \frac{1.5 \times 8.31 \times 450}{15 \times 10^{-3}} = 3.74 \times 10^5 \, \text{Pa} \approx 3.74 \, \text{atm}$.

Question 2

A gas has a $C_p$ of $20.8 \, \text{J mol}^{-1} \text{K}^{-1}$. What is the ratio of specific heats ($\gamma$)? ($R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}$)

Accepted Answer

$C_v = C_p - R = 20.8 - 8.31 = 12.49 \, \text{J mol}^{-1} \text{K}^{-1} \approx 12.5$. $\gamma = \frac{C_p}{C_v} = \frac{20.8}{12.5} \approx 1.66 \approx 1.67$.

Question 3

The mean free path of a gas is $1 \times 10^{-7} \, \text{m}$ with a molecular diameter of $2 \times 10^{-10} \, \text{m}$. What is the number density of the gas?

Accepted Answer

$l = \frac{1}{\sqrt{2} n \pi d^2}$, $n = \frac{1}{\sqrt{2} \pi d^2 l}$. $n = \frac{1}{1.414 \times 3.14 \times (2 \times 10^{-10})^2 \times 1 \times 10^{-7}} = \frac{1}{1.77 \times 10^{-26}} \approx 5.65 \times 10^{25} \, \text{m}^{-3}$.

NEET Physics: Behaviour of Perfect Gas and Kinetic Theory — Practice Set 15

Q1. A mixture of 1 mole of argon and 0.5 moles of nitrogen is at 450 K in a 15-litre container. What is the total pressure? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q2. A gas has a \(C_p\) of \(20.8 \, \text{J mol}^{-1} \text{K}^{-1}\). What is the ratio of specific heats (\(\gamma\))? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q3. The mean free path of a gas is \(1 \times 10^{-7} \, \text{m}\) with a molecular diameter of \(2 \times 10^{-10} \, \text{m}\). What is the number density of the gas?

Q4. At what temperature is the rms speed of nitrogen molecules 600 m/s? (Molecular mass of \(N_2 = 28 \, \text{u}\), \(k_B = 1.38 \times 10^{-23} \, \text{J K}^{-1}\))

Q5. What is the average translational kinetic energy of an oxygen molecule at 600 K? (\(k_B = 1.38 \times 10^{-23} \, \text{J K}^{-1}\))

Q6. A mixture of 0.5 moles of helium and 1.5 moles of oxygen is at 350 K in a 25-litre container. What is the total pressure? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q7. A gas has a density of \(1.2 \, \text{kg m}^{-3}\) at 2 atm and 400 K. What is its molecular mass? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\), 1 atm = \(1.01 \times 10^5 \, \text{Pa}\))

Q8. A gas at 400 K has a pressure of 1 atm. If the temperature is reduced to 200 K at constant volume, what is the new pressure?

Q9. What is the pressure of 0.8 moles of an ideal gas in a 16-litre container at 427°C? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q10. A gas at 1 atm and 273 K has a volume of 15 litres. If the temperature increases to 819 K at constant pressure, what is the new volume?