States Of Matter

To correctly match elements from Column - I with those in Column - II, we need to understand the concepts related to each term:

Root Mean Square (RMS) Speed of Gas Molecules: This is the measure of the average speed of particles in a gas and is given by the formula $%5Csqrt%7B%5Cfrac%7B3RT%7D%7BM%7D%7D$ , where $R$ is the gas constant, $T$ is the temperature, and $M$ is the molar mass of the gas. Thus, (A) matches with (Q).
The Pressure Exerted by the Ideal Gas: This is described by the kinetic theory of gases, where pressure $P$ is given as $%5Cfrac%7B1%7D%7B3%7Dnmv%5E2$ , where $n$ is the number of molecules per unit volume, $m$ is the mass of one molecule, and $v$ is the RMS speed. Thus, (B) matches with (P).
The Average Kinetic Energy of a Molecule: This is given by the formula $%5Cfrac%7B3%7D%7B2%7Dk_BT$ , where $k_B$ is Boltzmann's constant and $T$ is the temperature. Thus, (C) matches with (S).
The Total Internal Energy of 1 Mole of a Diatomic Gas: For a diatomic gas, the total internal energy is a function of the temperature and is given by $%5Cfrac%7B5%7D%7B2%7DRT$ for one mole. Thus, (D) matches with (R).

Therefore, the correct matching is:

Hence, the correct answer is: (A) - (Q), (B) - (P), (C) - (S), (D) - (R).

Chapter Questions
1 MCQs

Column - I		Column - II
(A)	Root mean square speed of gas molecules	(P)	$%5Cfrac%7B1%7D%7B3%7D$ nmv-²
(B)	The pressure exerted by the ideal gas	(Q)	$%5Csqrt%7B%5Cfrac%7B3%5C%2CRT%7D%7BM%7D%7D$
(C)	The average kinetic energy of a molecule	(R)	$%5Cfrac%7B5%7D%7B2%7DRT$
(D)	The total internal energy of 1 mole of a diatomic gas	(S)	$%5Cfrac%7B3%7D%7B2%7DkBT$