Match Molecular Kinetic Theory Quantities – Rankers Physics
Topic: Thermal Physics
Subtopic: Kinetic Theory of Gases

Match Molecular Kinetic Theory Quantities

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) \(\frac{1}{3} n m \bar{v}^2\) (Q) \(\sqrt{\frac{3RT}{M}}\) (R) \(\frac{5}{2} RT\) (S) \(\frac{3}{2} k_B T\)
 
(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)

Solution:

By kinetic theory: \(v_{\text{rms}} = \sqrt{\frac{3RT}{M}}\) -> (A)-(Q); Pressure \(P = \frac{1}{3} nm\bar{v}^2\) -> (B)-(P); Average KE \(= \frac{3}{2}k_BT\) -> (C)-(S); and Internal energy for diatomic gas \(= \frac{5}{2}RT\) -> (D)-(R).

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