Match the Column-I and Column-II and choose the correct match from the given column.
Column-I - Column-II
(A) Root mean square speed of gas molecules → (P) \(\frac{1}{3}\)nmv-2
(B) Pressure exerted by ideal gas → (Q) \(\sqrt{\frac{3RT}{M}}\)
(C) Average kinetic energy of a molecule → (R) \(\frac{5}{2}RT\)
(D) Total internal energy of 1 mole of a diatomic gas → (R) \(\frac{3}{2}k_BT\)
(1) (A) - (R), (B) - (P), (C) - (S), (D) - (Q)
(2) (A) - (Q), (B) - (R), (C) - (S), (D) - (P)
(3) (A) - (Q), (B) - (P), (C) - (S), (D) - (R)
(4) (A) - (R), (B) - (Q), (C) - (P), (D) - (S)
Correct answer: (3) (A) - (Q), (B) - (P), (C) - (S), (D) - (R)
Explanation:
Root mean square speed of gas molecules
vrms = \(\sqrt{\frac{3RT}{M}}\)
Pressure exerted by ideal Gas
P = \(\frac{1}{3}\rho v^2_{rms}\)
P = \(\frac{1}{3}mnv^2\)
ρ = mn, v2rms = \(\bar v^2\)
Average kinetic energy of a molecular
KE = \(\frac{3}{2}KT\)
Total internal energy of 1 mole of a diatomic gas
U = \(\frac{f}{2}\mu RT\)
U = \(\frac{5}{2}RT\)(For 1 mole diatomic gas)