Chapter 4, Problem 4.1DQ

(a)

Interpretation Introduction

Interpretation:

Chemical potential vary with temperture, the reason behind this has to be given.

Concept introduction:

Chemical potential:

The chemical potential tell us how the Gibbs Free energy will vary with the number of moles $n_i$ of component I holding temperature, pressure, and the number of moles of all other components constant. For a pure substance, the chemical potential is equal to its molar Gibbs Free energy.

${\text{μ}}_{\text{i}}\text{=}{\left(\frac{\partial \text{G}}{\partial {\text{n}}_{\text{i}}}\right)}_{{\text{T,P,n}}_{\text{i,j}}}\boxed{\begin{array}{l}\text{where,}\\ {\text{μ}}_{\text{i}}\text{Chemical}\text{potential}\\ \text{G}\text{Gibbs}\text{free}\text{energy}\\ \text{T}\text{Temperature}\\ \text{P}\text{Pressure}\end{array}}$

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.  All spontaneous process is associated with the decrease of free energy in the system.  The equation given below helps us to calculate the change in free energy in a system.

  $\text{ΔG = }\Delta {\rm H}\text{- T}\Delta \text{S}$

Where,

  $\text{ΔG }$ is the change in free energy of the system

  $\Delta {\rm H}$ is the change in enthalpy of the system

  $\text{T}$ is the absolute value of the temperature

  $\Delta \text{S}$ is the change in entropy in the system

Enthalpy H is the amount energy absorbed or released in a process.

$\text{Enthalpy}H=U+PV\boxed{\begin{array}{l}\text{Where,}\\ \text{U}\text{:}\text{internal}\text{energy}\\ \text{P}\text{:}\text{pressure}\\ \text{V}\text{:}v\text{olume}\end{array}}$

(b)

Interpretation Introduction

Interpretation:

Chemical potential vary with pressure, the reason behind this has to be given.

Concept introduction:

Chemical potential:

The chemical potential tell us how the Gibbs Free energy will vary with the number of moles $n_i$ of component I holding temperature, pressure, and the number of moles of all other components constant. For a pure substance, the chemical potential is equal to its molar Gibbs Free energy.

${\text{μ}}_{\text{i}}\text{=}{\left(\frac{\partial \text{G}}{\partial {\text{n}}_{\text{i}}}\right)}_{{\text{T,P,n}}_{\text{i,j}}}\boxed{\begin{array}{l}\text{where,}\\ {\text{μ}}_{\text{i}}\text{Chemical}\text{potential}\\ \text{G}\text{Gibbs}\text{free}\text{energy}\\ \text{T}\text{Temperature}\\ \text{P}\text{Pressure}\end{array}}$

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.  All spontaneous process is associated with the decrease of free energy in the system.  The equation given below helps us to calculate the change in free energy in a system.

  $\text{ΔG = }\Delta {\rm H}\text{- T}\Delta \text{S}$

Where,

  $\text{ΔG }$ is the change in free energy of the system

  $\Delta {\rm H}$ is the change in enthalpy of the system

  $\text{T}$ is the absolute value of the temperature

  $\Delta \text{S}$ is the change in entropy in the system

Enthalpy H is the amount energy absorbed or released in a process.

$\text{Enthalpy}H=U+PV\boxed{\begin{array}{l}\text{Where,}\\ \text{U}\text{:}\text{internal}\text{energy}\\ \text{P}\text{:}\text{pressure}\\ \text{V}\text{:}v\text{olume}\end{array}}$