Chapter 7, Problem 7.46P

(a)

Interpretation Introduction

Interpretation:

To prove that ${(\frac{\partial Z}{\partial T})}_P=0$

Concept Introduction:

The mathematical expression is:

  $\mu ={(\frac{\partial T}{\partial P})}_H=0$

By Real Gas Equation of State where,

P = Pressure

V = Volume

R = Universal Gas Constant

T = Temperature

Z = Compressibility Factor

  $PV=ZRT$

(b)

Interpretation Introduction

Interpretation:

To prove that ${(\frac{\partial H}{\partial P})}_T=0$

Concept Introduction:

The Joule Thompson Inversion curve is given as below: -

  $\mu ={(\frac{\partial T}{\partial P})}_H=0$

(c)

Interpretation Introduction

Interpretation:

To prove that ${(\frac{\partial V}{\partial T})}_P=\frac{V}{T}$

Concept Introduction:

The Joule Thompson Inversion curve is given as below: -

  $\mu ={(\frac{\partial T}{\partial P})}_H=0$

By Defination C_{P =}${(\frac{\partial H}{\partial T})}_P$

Equation for enthalpy change at constant temperature is given as ${(\frac{\partial H}{\partial P})}_T=[V-T{(\frac{\partial V}{\partial T})}_P]$

(d)

Interpretation Introduction

Interpretation:

To prove that ${\left(\frac{\partial Z}{\partial V}\right)}_P=0$

Concept Introduction:

The Joule Thompson Inversion curve is given as below: -

  $\mu ={(\frac{\partial T}{\partial P})}_H=0$

And from sub part (a), ${\left(\frac{\partial Z}{\partial T}\right)}_P=0$

(e)

Interpretation Introduction

Interpretation:

To prove that, $V{\left(\frac{\partial P}{\partial V}\right)}_T+T{\left(\frac{\partial P}{\partial T}\right)}_V=0$

Concept Introduction:

The Joule Thompson Inversion curve is given as below: -

  $\mu ={(\frac{\partial T}{\partial P})}_H=0$

Definition of enthalpy is as given below,

  $dH=TdS+VdP$

Maxwell Relation, ${\left(\frac{\partial V}{\partial T}\right)}_P=-{\left(\frac{\partial S}{\partial P}\right)}_T$