Question

Match Column - I and Column - II and choose the correct match from the given choices. 

Column - I		Column - II
(A)	Root mean square speed of gas molecules	(P)	\(\frac{1}{3}\) nmv-2
(B)	The pressure exerted by the ideal gas	(Q)	\(\sqrt{\frac{3\,RT}{M}}\)
(C)	The average kinetic energy of a molecule	(R)	\(\frac{5}{2}RT\)
(D)	The total internal energy of 1 mole of a diatomic gas	(S)	\(\frac{3}{2}kBT\)

• (A) - (R), (B) - (Q), (C) - (P), (D) - (S)
• (A) - (R), (B) - (P), (C) - (S), (D) - (Q)
• (A) - (Q), (B) - (R), (C) - (S), (D) - (P)
• (A) - (Q), (B) - (P), (C) - (S), (D) - (R)

Answer 1

The Correct Option is D

To correctly match elements from Column - I with those in Column - II, we need to understand the concepts related to each term:

1. Root Mean Square (RMS) Speed of Gas Molecules: This is the measure of the average speed of particles in a gas and is given by the formula \(\sqrt{\frac{3RT}{M}}\), where \(R\) is the gas constant, \(T\) is the temperature, and \(M\) is the molar mass of the gas. Thus, (A) matches with (Q).
2. The Pressure Exerted by the Ideal Gas: This is described by the kinetic theory of gases, where pressure \(P\) is given as \(\frac{1}{3}nmv^2\), where \(n\) is the number of molecules per unit volume, \(m\) is the mass of one molecule, and \(v\) is the RMS speed. Thus, (B) matches with (P).
3. The Average Kinetic Energy of a Molecule: This is given by the formula \(\frac{3}{2}k_BT\), where \(k_B\) is Boltzmann's constant and \(T\) is the temperature. Thus, (C) matches with (S). 
4. The Total Internal Energy of 1 Mole of a Diatomic Gas: For a diatomic gas, the total internal energy is a function of the temperature and is given by \(\frac{5}{2}RT\) for one mole. Thus, (D) matches with (R).

Therefore, the correct matching is:

• (A) - (Q)
• (B) - (P)
• (C) - (S)
• (D) - (R)

Hence, the correct answer is: (A) - (Q), (B) - (P), (C) - (S), (D) - (R).