A sealed syringe traps air at absolute pressure 140 kPa and volume 92 cm³. It is compressed slowly to 55.2 cm³ and allowed to return to its original temperature. (a) Calculate its final absolute pressure. (b) Explain the change using particle collisions. (c) Explain why measuring immediately after a rapid compression could give a different result.

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233.3 kPa; more frequent wall collisions; rapid compression can temporarily heat the gas and increase the pressure further. The amount of gas is fixed and the final temperature equals the initial temperature. For these conditions pressure is inversely proportional to volume, so p₁V₁ = p₂V₂ using absolute pressures. Rearrange to p₂ = p₁V₁/V₂ = 140 × 92/55.2 = 233.3 kPa. The same volume units occur above and below the fraction and cancel. At the same temperature, the average particle kinetic energy is unchanged. The particles have less distance to travel between walls, so collisions with a given area of wall occur more frequently and transfer momentum more often. Rapid compression involves work being done on the gas before much energy can escape. Its temperature may rise, increasing average particle speed and pressure. Wait for thermal equilibrium, keep the syringe sealed, and avoid confusing gauge pressure with the stated absolute pressure.

Slow compression of trapped air 9

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