A triple point is invariant because it represents a unique condition where three phases are in equilibrium, and any deviation in pressure or temperature from this specific point causes one or more phases to disappear.
A triple point is a specific pressure and temperature condition where three distinct phases of a substance can coexist in stable equilibrium. Think of it as a junction where three stability fields meet and overlap perfectly.
According to the reference provided, a triple point, like Point C, is located where three stability fields intersect. This particular condition is described by the phase rule, which for a single-component system (like pure water) is typically expressed as F = C - P + 2, where F is variance, C is the number of components, and P is the number of phases. At the triple point for a single component, C=1 and P=3. Applying the phase rule (as referenced: 3 + F = 1 + 2, which implies F = 0), the variance (F) is 0.
Variance and Invariance Explained
- Variance (F): This number indicates the degrees of freedom, or the number of intensive variables (like temperature or pressure) that can be independently changed without altering the number of phases present.
- Invariant Point: A point with zero variance (F=0). At such a point, no variables can be independently changed while maintaining the current phase equilibrium.
Why Changing Conditions Matters
The core reason a triple point is an invariant point is explicitly stated in the reference: a change in either pressure or temperature results in the loss of one or more phases.
Consider the triple point for water, where solid ice, liquid water, and water vapor coexist.
- If you slightly increase the temperature while holding pressure constant at the triple point pressure, the ice will melt, and the vapor might condense or increase depending on the exact path, but you will no longer have all three phases simultaneously in equilibrium.
- If you slightly increase the pressure while holding temperature constant at the triple point temperature, the vapor will condense into liquid, and the ice might melt or remain depending on pressure's effect on melting point, but again, you lose the simultaneous presence of all three phases.
Since you cannot change either pressure or temperature even slightly without causing one or more of the three coexisting phases to vanish, the triple point represents a fixed, unchangeable condition for that substance where all three phases are stable together. This makes it unique and invariant.
This invariance is why triple points are often used as fixed reference points for calibrating thermometers and pressure gauges. For example, the triple point of water (at 0.01 °C and 611.657 Pascals) is a precisely defined standard.
