Kinetic Theory

JEE Main level, single correct, medium

136 of 168

Question 136 of 168

Following statements are given
(1) The average kinetic energy of a gas molecule decreases when the temperature is reduced.

(2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.

(3) The average kinetic energy of a gas molecule decreases with increases in volume.

(4) Pressure of a gas increases with increase in temperature at constant volume.

(5) The volume of gas decreases with increase in temperature.

Choose the correct answer from the options given below :

Show answer and solution

Answer: (A) (1) and (4) only

Average kinetic energy of a gas molecule is given by KEavg=32KT{KE}_{avg}=\dfrac{3}{2}KT.
Pressure of a gas in terms of rms speed is given by
P=13ρvrms2P=\dfrac{1}{3}\rho {v}_{rms}^{2}.
As
KEavg∝TK{E}_{avg}\propto T, so (1)\left(1\right) is correct, (2)\left(2\right) is incorrect, statement (3)\left(3\right) can not be said.
Note : Statement (4) is correct only if we consider it at constant volume and not constant pressure. Ideally, this question must be bonus but most appropriate answer is option (A)

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