At atmospheric pressure, a material of unknown composition shows three phases in equilibrium at 710°C. The minimum number of components in the system will be:

Explanation:

According to the phase rule in thermodynamics, the minimum number of components in a system can be determined using the Gibbs phase rule. The Gibbs phase rule is given by the formula:

F = C - P + 2

Where:

• F is the number of degrees of freedom (independent variables like temperature, pressure, and composition).
• C is the number of components in the system.
• P is the number of phases in equilibrium.

In the given problem, it is stated that a material of unknown composition shows three phases in equilibrium at atmospheric pressure (constant pressure) at 710°C. Thus, the number of phases (P) is 3.

Since the pressure is constant (atmospheric pressure), the degrees of freedom (F) will be 1 (temperature only).

Substituting these values into the Gibbs phase rule equation, we get:

F = C - P + 2

⇒ 1 = C - 3 + 2

⇒ 1 = C - 1

⇒ C = 2