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) $\dfrac{1}{3}nm\bar{v}^2$
(Q) $\sqrt{\dfrac{3RT}{M}}$
(R) $\dfrac{5}{2}RT$
(S) $\dfrac{3}{2}k_BT$
Answer: (D) (A)-(Q), (B)-(P), (C)-(S), (D)-(R)
(A) $v_{rms} = \sqrt{\dfrac{3RT}{M}}$ (Q).
(B) Pressure: $P = \dfrac{1}{3}nm\bar{v}^2$ (P).
(C) Average (translational) kinetic energy of a molecule: $\dfrac{3}{2}k_BT$ (S).
(D) Internal energy of 1 mole of a diatomic gas (5 degrees of freedom): $\dfrac{5}{2}RT$ (R).
(A)-(Q), (B)-(P), (C)-(S), (D)-(R).
Solution by Sreeraj P, M.Sc Physics