Match Column-I with Column-II. 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: (i) (1/3)nm⟨v²⟩; (ii) √(3RT/M); (iii) (5/2)RT; (iv) (3/2)kBT. Choose the correct matching:
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Question

Match Column-I with Column-II. 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: (i) (1/3)nm⟨v²⟩; (ii) √(3RT/M); (iii) (5/2)RT; (iv) (3/2)kBT. Choose the correct matching:

Options

G1 Physics · Accepted Answer

Step 1: RMS speed of gas molecules: vRMS = √(3RT/M), so (a) → (ii). Step 2: Pressure from molecular collisions: P = (1/3)nm⟨v²⟩, so (b) → (i), with n number density. Step 3: Mean translational kinetic energy per molecule: ⟨K⟩ = (3/2)kBT, so (c) → (iv). Step 4: For one mole of diatomic ideal gas (vibrations neglected), U = (5/2)RT, so (d) → (iii). Step 5: Matching: (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii). Final answer: (C).