On boiling, water becomes a vapor, liquid volume decreases and vapour volume increases. Since volumes are not constant, how do we call it as equilibrium?

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    $\begingroup$ Stop applying heat to it, and wait a bit until the boiling ceases. Now that's an equilibrium. $\endgroup$ – Ivan Neretin Feb 20 '16 at 7:49
  • $\begingroup$ but in equilibrium means that they should be constant know? but is liquid and vapor constant on boiling point? they are changing then how can we call it as equilibrium? $\endgroup$ – Selvaratnam Lavinan Feb 20 '16 at 10:21
  • $\begingroup$ If you keep heating it nonstop then obviously the temperature will continue to increase beyond the boiling point. Once the temperature is higher than that it is no longer at equilibrium. $\endgroup$ – orthocresol Feb 20 '16 at 13:18
  • $\begingroup$ You are correct. The system is not quite at equilibrium when you are adding heat to it and the water is boiling. However, the liquid and bubble temperatures and pressures below the liquid surface are very close to the equilibrium values. In my judgment, @aventurin 's concise answer below is right on target. $\endgroup$ – Chet Miller Feb 20 '16 at 15:15

An isolated system consisting of liquid water and vapour is always in equilibrium.

If you are applying heat to a system consisting of liquid water and vapour the system is not in equilibrium.

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I will give you an answer that doesn't rely with microscopic variables or statistical physics.

There is a misconception about equilibrium definition. Equilibrium is different of "a particular definition equilibrium state". We define the thermodynamic state of a simple system with a function of few macroscopic variables. For example S(E,V,N) (entropy, energy, volume and lets say mass). But you also can define it in therms of (more useful in the context of the question) the Gibbs free energy (G), G = G(T,P,N). In such case the state specification does not require the volume. If you have a composite system in the circumstances that you described (or two phases), you have (for system 1 and 2)

$$ G = G_1 + G_2 = G_1(T,P,N_1)+G_2(T,P,N_2) $$

but as $G$ is an homogeneous function it is trivial to prove that the sum remains constant so we have a lot of states of the composite system with the same total free energy, that it is in fact the minimum energy that the composite system can have.

Then by the incorrect usage of the language we call this set of states "equilibrium state".

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