NEET Behaviour of Perfect Gas and Kinetic Theory — Set 3

Question 1

What is the total internal energy of 1 mole 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 (3 translational + 3 rotational). $U = 3 R T = 3 \times 8.31 \times 300 = 7479 \, \text{J} \approx 7.48 \, \text{kJ}$.

Question 2

How much heat is required to raise the temperature of 0.2 moles of a diatomic gas by 10 K at constant volume, with no vibrational modes? ($R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}$)

Accepted Answer

Diatomic gas: 5 degrees of freedom, $C_v = \frac{5}{2} R$. $Q = \mu C_v \Delta T = 0.2 \times \frac{5}{2} \times 8.31 \times 10 = 83.1 \, \text{J}$.

Question 3

How much heat is required to raise the temperature of 0.4 moles of a triatomic gas by 15 K at constant volume, with no vibrational modes? ($R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}$)

Accepted Answer

Triatomic gas: 6 degrees of freedom, $C_v = 3 R$. $Q = \mu C_v \Delta T = 0.4 \times 3 \times 8.31 \times 15 = 149.58 \, \text{J} \approx 149.6 \, \text{J}$.

NEET Physics: Behaviour of Perfect Gas and Kinetic Theory — Practice Set 3

Q1. What is the total internal energy of 1 mole of a triatomic gas at 300 K with no vibrational modes? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q2. How much heat is required to raise the temperature of 0.2 moles of a diatomic gas by 10 K at constant volume, with no vibrational modes? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q3. How much heat is required to raise the temperature of 0.4 moles of a triatomic gas by 15 K at constant volume, with no vibrational modes? (\(R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1}\))

Q4. A gas occupies a volume of 11.2 litres at STP. How many molecules are present in this gas? (\(N_A = 6.02 \times 10^{23} \, \text{mol}^{-1}\))

Q5. At STP, 22.4 litres of oxygen gas (\(O_2\)) is present. What is the mass of this gas? (Molecular mass of \(O_2 = 32 \, \text{u}\), \(1 \, \text{u} = 1 \, \text{g/mol}\))

Q6. A gas occupies 56.0 litres at STP. How many moles are present? (Molar volume at STP = 22.4 litres)

Q7. A gas at 3 atm and 400 K has a volume of 15 litres. If the pressure drops to 1.5 atm at constant temperature, what is the new volume?

Q8. A gas occupies 67.2 litres at STP. How many molecules are present? (\(N_A = 6.02 \times 10^{23} \, \text{mol}^{-1}\), molar volume at STP = 22.4 litres)

Q9. At what temperature is the rms speed of helium molecules 1500 m/s? (Atomic mass of He = 4 u, \(k_B = 1.38 \times 10^{-23} \, \text{J K}^{-1}\))

Q10. What is the collision frequency of a gas molecule with a mean free path of \(3.0 \times 10^{-7} \, \text{m}\) and average speed of 600 m/s?