Chapter 4, Problem 4.15P

Interpretation Introduction

Interpretation:

Calculate the heat exchanger duty in $\text{kW}$ for methanol if one hundred kmol per hour of its sub cooled liquid at $\text{300}\text{K}$ and $\text{3}\text{bar}$ is superheated to $\text{500}\text{K}$ in a steady flow heat exchanger.

Concept Introduction :

Since methanol is converted to its subcooled form to superheated form, it will go through vaporization after reaching its saturation temperature, so total heat required to change the phase will be

  $\begin{array}{l}Q=\text{sensible heat required to change temperature of subcooled liquid to saturation temperature}\\ \text{+Latent heat liberated due to phase change}\\ \text{+sensible heat required to change saturation temperature to temperature of superheated liquid }\end{array}$

The sensible heat in steady-flow exchangers for agas is calculated as:

  $Q=\Delta H=R{\displaystyle \underset{T_0}{\overset{T}{\int }}\frac{\Delta C_P}{R}dT}$......(1)

Where $\Delta H$ is heat of reaction at any temperature $T$ .

and

  ${\displaystyle \underset{T_0}{\overset{T}{\int }}\frac{\Delta C^{\circ }{}_P}{R}dT}=A{T}_0(\tau -1)+\frac{B}{2}{T}_0{}^2({\tau }^2-1)+\frac{C}{3}{T}_0{}^3({\tau }^3-1)+\frac{D}{T_0}(\frac{\tau -1}{\tau })$......(2)

Where $\tau =\frac{T}{T_0}$

And latent heat or heat of vaporization at any temperature from known value at a single temperature is calculated as:

  $\frac{\Delta H_n}{R{T}_n}=\frac{1.092(\ln P_C-1.013)}{0.93-T_{rn}}$

And

  $\frac{\Delta H_2}{\Delta H_1}={\left(\frac{1-T_{r2}}{1-T_{r1}}\right)}^{0.38}$