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PRACTICE / Adiabatic processes

A partition cannot deliver piston work

Identical ideal-gas samples initially have pV = 200 J. Each reaches twice its initial volume and the same final temperature as initially. Sample A expands reversibly and isothermally. Sample B expands into vacuum inside an insulated rigid enclosure.

How much more work by the gas does A deliver than B?

Organize the givens & assumptions
  • Initial pV = 200 J
  • Vf/Vi = 2
  • B: insulated partition removal into vacuum

Closed fixed amount of ideal gas, constant stated heat capacities, negligible bulk kinetic and gravitational energy changes, and only pressure–volume work. Heat into the gas and work by the gas are positive.

  1. A0 J0\ \mathrm J
  2. B200 J200\ \mathrm J
  3. C−200ln⁡2 J-200\ln2\ \mathrm J
  4. D200ln⁡2 J200\ln2\ \mathrm J

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