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Match Column - I and Column - II and choose the correct match from the given choices. Column - I: (A) Root mean square speed of gas molecules, (B) Pressure exerted by ideal gas, (C) Average kinetic energy of a molecule, (D) Total internal energy of 1 mole of a diatomic gas. Column - II: (P) 13nmvˉ2\frac{1}{3}nm\bar{v}^2, (Q) 3RTM\sqrt{\frac{3RT}{M}}, (R) 52RT\frac{5}{2}RT, (S) 32kBT\frac{3}{2}k_BT.

A

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

B

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

C

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

D

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

Step-by-Step Solution

Root mean square speed of gas molecules is 3RTM\sqrt{\frac{3RT}{M}} (A-Q). Pressure exerted by ideal gas is 13nmvˉ2\frac{1}{3}nm\bar{v}^2 (B-P). Average kinetic energy of a molecule is 32kBT\frac{3}{2}k_BT (C-S). Total internal energy of 1 mole of a diatomic gas is 52RT\frac{5}{2}RT (D-R). Thus, the correct match is (A)-(Q), (B)-(P), (C)-(S), (D)-(R).

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