A rigid sealed canister contains gas at 100 kPa and 290 K. It is heated to 348 K. (a) Calculate final pressure. (b) Explain the change using particles. (c) Explain the difference with a freely moving piston. (d) State two reasons the ideal particle model may fail at very high pressure.

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Final pressure 120 kPa; faster particles collide more often and transfer more momentum. A moving piston permits expansion. At fixed amount and rigid volume, p/T is constant using kelvin temperatures. Therefore p₂ = 100 × 348/290 = 120 kPa. Heating increases mean molecular kinetic energy and speed. Particles reach the walls more frequently and each collision generally transfers more momentum, increasing force per area. Kelvin temperature must be used because it is proportional to mean kinetic energy. A Celsius ratio would imply 0 °C means no molecular motion. A freely moving piston allows volume to increase and can keep pressure near external pressure during slow motion; some heating then supplies boundary work. At high pressure, molecular volume is not negligible and intermolecular forces affect motion, violating ideal assumptions of point particles and no forces except elastic collisions.

Heating gas in a rigid canister

A rigid sealed canister contains gas at 100 kPa and 290 K. It is heated to 348 K. (a) Calculate final pressure. (b) Explain the change using particles. (c) Explain the difference with a freely moving piston. (d) State two reasons the ideal particle model may fail at very high pressure.

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