Problem — Ranking pressures by temperature

Problem

Ranking pressures. Four identical containers hold $n$ moles of the same gas at temperatures: (A) $T = 200$ K; (B) $T = 273$ K; (C) $T = 350$ K; (D) $T = 600$ K. Order the pressures from lowest to highest.

Solution

The containers are identical (same volume $V$) and hold the same number $n$ of moles. From the ideal gas law $pV = nRT$, with $V$ and $n$ fixed, the pressure is directly proportional to the absolute temperature: $p = \frac{nR}{V}\,T \propto T$ So it suffices to order by increasing temperature. Since $T_A = 200 < T_B = 273 < T_C = 350 < T_D = 600$ K, the pressures follow the same order: $\ev{A < B < C < D}$

Links

Topics: Kinetic theory of gases Concepts: Ideal gas law · Pressure Skills: Ranking reasoning