If a system has cind independent components, what is the maximum number of phases that can exist in equilibrium? (b) A given system has eight liquid phases in equilibrium with each other. What must be true about the number of independent components in this system?

We know that, The degree of freedom f for a system can be simply referred to as number of variables that must be defined to completely solve a system.

If degree of freedom is 0, then any problem is can be solved.

a) If a system has cind independent components, what is the maximum number of phases that can exist in equilibrium?

The degree of freedom for a system can be written as;

f = [tex]c_{ind[/tex] - p + 2

where f is the degree of freedom

[tex]c_{ind[/tex] is the number of independent component

so we solve for [tex]c_{ind[/tex]

[tex]c_{ind[/tex] = f + p - 2

we know that f can not be less than 0

Hence maximum possible face will be;

[tex]c_{ind[/tex] = p - 2

p = [tex]c_{ind[/tex] + 2

Therefore, the maximum number of phases that can exist in equilibrium is [tex]c_{ind[/tex] + 2

b) A given system has eight liquid phases in equilibrium with each other. What must be true about the number of independent components in this system?

Number of phases in the system p = 8

p = [tex]c_{ind[/tex] + 2

[tex]c_{ind[/tex] = p - 2

we substitute

[tex]c_{ind[/tex] = 8 - 2

[tex]c_{ind[/tex] = 6

Therefore, the number of independent components in this system are 6