Chapter 7, Problem 7.1E

Interpretation Introduction

Interpretation:

The degree of freedom for the given system on addition of olive is to be stated.

Concept introduction:

The degree of freedom can be defined as the variables used to define a system which is at equilibrium. This can be determined using Gibbs rule which is given below.

$\text{F}=\text{C}-\text{P}+2$

In the above equation, F is the degree of freedom, C is number of components present in system and P is the number of phases in the system.

Answer to Problem 7.1E

The degree of freedom of the water and ethanol system on addition of olive is $3$.

Explanation of Solution

The example $7.1$ has a system of two components that is ethanol and water. On addition of olive, number of components becomes $3$. Ethanol and water are in the same phase but olive is in a different phase. Therefore, the number of phases becomes equal to $2$. On substitution of these values in Gibbs rule, degree of freedom obtained is given below.

$\begin{array}{rll}\text{F }& =& \text{ 3}-\text{2}+\text{2}\\ & =& \text{ 3}\end{array}$.

Thus, the variables selected for determining degree of freedom are phases and number of components.

Conclusion

The degree of freedom of the ethanol and water system on addition of olive is $3$.