Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

Match Column-I and Column-II and choose the correct match from the given choices.

Column-I (P) Root mean square speed of gas molecules (Q) The pressure exerted by an ideal gas (R) The average kinetic energy of a molecule (S) The total internal energy of a mole of a diatomic gas

Column-II (1) $\frac{1}{3}nm\bar{v}^2$ (2) $\sqrt{\frac{3RT}{M}}$ (3) $\frac{5}{2}RT$ (4) $\frac{3}{2}k_BT$

P-1, Q-2, R-3, S-4

P-2, Q-1, R-4, S-3

P-3, Q-4, R-1, S-2

P-4, Q-3, R-2, S-1

Step-by-Step Solution

Root Mean Square Speed ( $v_{rms}$ ): The formula for the RMS speed of an ideal gas is $v_{rms} = \sqrt{\frac{3RT}{M}}$ . Thus, (P) matches with (2).
Pressure ( $P$ ): According to the kinetic theory, pressure is given by $P = \frac{1}{3}nm\bar{v}^2$ , where $n$ is number density and $m$ is mass of a molecule. Thus, (Q) matches with (1).
Average Kinetic Energy per Molecule ( $E$ ): The average translational kinetic energy per molecule depends only on temperature and is given by $E = \frac{3}{2}k_BT$ . Thus, (R) matches with (4).
Internal Energy of a Diatomic Gas ( $U$ ): A diatomic gas has 5 degrees of freedom ( $f=5$ ) at moderate temperatures (3 translational + 2 rotational). The internal energy per mole is $U = \frac{f}{2}RT = \frac{5}{2}RT$ . Thus, (S) matches with (3).

Conclusion: P-2, Q-1, R-4, S-3.

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