Question

How many degrees of freedom are there at the triple point in a one-component system?

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

The triple point of any pure substance is invariant ($F=0$). It occurs strictly at one specific, unalterable temperature and pressure uniquely characteristic of that substance.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We need to calculate the degrees of freedom for a one-component system existing exactly at its triple point using Gibbs Phase Rule.
Step 2: Key Formula or Approach:
Gibbs Phase Rule relates the degrees of freedom ($F$), the number of components ($C$), and the number of phases in equilibrium ($P$) mathematically: \[ F = C - P + 2 \] Step 3: Detailed Explanation:
From the problem description:
The system is a "one-component system", therefore $C = 1$ (e.g., pure water).
The system is at its "triple point". By definition, a triple point is the unique temperature and pressure where three phases (solid, liquid, and gas) coexist in mutual thermodynamic equilibrium. Therefore, the number of phases $P = 3$.
Substitute these values into the Phase Rule: \[ F = 1 - 3 + 2 \] \[ F = 0 \] A degree of freedom of 0 means the system is "invariant". Neither pressure nor temperature can be changed without disrupting the equilibrium and losing at least one of the three phases.
Step 4: Final Answer:
There are 0 degrees of freedom at the triple point.