Statement 1: At constant volume, the pressure of a fixed amount of an ideal gas is proportional to its absolute temperature.
Statement 2: Frequency of collisions and their impact both increase in proportion to the square root of absolute temperature.

Question

Statement 1: At constant volume, the pressure of a fixed amount of an ideal gas is proportional to its absolute temperature.

Statement 2: Frequency of collisions and their impact both increase in proportion to the square root of absolute temperature.

TestHub · Accepted Answer

Statement 1 is the pressure-temperature (Amontons) law, correct. In Statement 2, wall-collision frequency ∝ barv ∝ √(T) (number density is fixed at constant V) and impulse per collision ∝ mbarv ∝ √(T); both claims are correct. Pressure = (collision frequency per unit area) × (impulse per collision) ∝ √(T) × √(T) = T, which is precisely Statement 1 — II is the kinetic derivation of I. Ans: (a).

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