Triple Point

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victorias

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Is there any phase change actually happening at the triple point?

I know that the three phases solid, liquid and gas exist in equilibrium at this point - does that mean that all possible types of phase changes (boiling, melting, vaporization, condensation, sublimation, deposition) are actually happening at this point but that the rate of each type is in equilibrium thus, no net change in the amount of solid, liquid and gas form.

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Yes. You are exactly right. This is the concept of dynamic equilibrium - sublimation is occurring at the same rate as deposition, etc. so that there is no net change in composition and all three phases co-exist happily.
 
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