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In a grand canonical ensemble, a system X of fixed volume is in contact with a large reservoir Y, then :

  • A.X can exchange only energy with Y
  • B.X can exchange only particles with Y
  • C.X can exchange neither energy nor particles with Y
  • D.X can exchange both energy and particles with Y

Answer: D

In a grand canonical ensemble, X can exchange both energy and particles with Y.

The three standard ensembles differ in what the system shares with its surroundings. A microcanonical ensemble (fixed N, V, E) is isolated. A canonical ensemble (fixed N, V, T) exchanges energy with a heat reservoir but not particles. A grand canonical ensemble (fixed μ, V, T) exchanges both energy and particles with a reservoir, which fixes the temperature and the chemical potential while N and E fluctuate.

Exchange of energy only is the canonical case, exchange of neither is the microcanonical case, and particle exchange without energy exchange is not one of the standard ensembles.

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