The isothermal expansion of an ideal gas into a vacuum is an irreversible proces

Question

The isothermal expansion of an ideal gas into a vacuum is an irreversible process. Briefly explain your answer. A reversible compression will require less PV work input than will an irreversible compression (between the same initial and final states as for the reversible process). Briefly explain your answer, including a labelled sketch of a PV indicator diagram that compares work input for reversible compression vs. irreversible compression (using constant external pressure), between the same initial and final states.

Explanation / Answer

The isothermal expansion of an ideal gas into a vacuum is an irreversible process. The statement given is false.

In an isothermal expansion, heat is allowed to flow into or out of the system so that temperature remains constant throughout the process of expansion. Since, for an ideal gas, the internal energy, depends only on temperature, it follows that at constant temperature, the internal energy of the gas remains constant, i.e., E is zero. For, E = 0, q = -w.

This shows that in isothermal expansion, the work is done by the system at the expense of heat absorbed. The magnitude of q or w depends on the manner in which the process of expansion is carried reversibly or irreversibly.

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