Chapter 8, Problem 8.68P

Interpretation Introduction

(a)

Interpretation:

The mass flowrate and composition of the product streams are to be calculated.

Concept introduction:

A flowchart is the complete representation of a process through boxes or other shapes which represents process units and arrows that represents the input and output of the process. The flowchart must be fully labelled to infer important data about the process involved.

In a system, a conserved quantity (total mass, mass of a particular species, energy or momentum) is balanced and can be written as:

$input+generation-output-consumpumtion=accumulation$

Here, ‘input’ is the stream which enters the system. ‘generation’ is the term used for the quantity that is produced within the system. ‘output’ is the stream which leaves the system. ‘consumption’ is the term used for the quantity that is consumed within the system. ‘accumulation’ is used for the quantity which is builds up within the system.

All the equations which are formed are then solved simultaneously to calculate the values of the unknown variables.

Mass fraction $\left(x_i\right)$ of any component is given by:

$x_i=\frac{{\dot{m}}_i}{\sum {\dot{m}}_i}$

             …… (1)

Here, ${\dot{m}}_i$ is the mass flowrate of the component $i$ and $\sum {\dot{m}}_i$ is the total mass flowrate of all the components present in the mixture.

Interpretation Introduction

(b)

Interpretation:

The cooling requirement of condenser, ${\dot{Q}}_c\text{ kJ/h}$, is to be calculated.

Concept introduction:

According to the Hess’s law, the total enthalpy for a reaction is the sum of all the changes in the multiple steps of the reaction. According to this law, enthalpy is a state function.

Specific enthalpy $\left(\hat{H}\right)$ of any substance at temperature $T^{\circ }\text{C}$ is given by:

$\hat{H}={\int }_{T_{ref}}^T{C}_{p}dT$

             …… (2)

Here, $T_{ref}$ is the reference temperature taken for the calculations.

The rate of heat transfer is calculated as:

$\dot{Q}=\dot{m}\Delta \hat{H}$

             …… (3)

Interpretation Introduction

(c)

Interpretation:

The heating requirement of reboiler is to be calculated using overall energy balance.

Concept introduction:

In a system, a conserved quantity (total mass, mass of a particular species, energy or momentum) is balanced and can be written as:

$input+generation-output-consumpumtion=accumulation$

Here, ‘input’ is the stream which enters the system. ‘generation’ is the term used for the quantity that is produced within the system. ‘output’ is the stream which leaves the system. ‘consumption’ is the term used for the quantity that is consumed within the system. ‘accumulation’ is used for the quantity which is builds up within the system.

All the equations which are formed are then solved simultaneously to calculate the values of the unknown variables.

The equation for energy balance is:

$\Delta H+\Delta E_{\text{k}}+\Delta E_{\text{p}}=Q-W_{\text{s}}$

             …… (4)

Here, $\Delta H$ is the change in the enthalpy of the system, $\Delta E_{\text{k}}$ is the kinetic energy change of the system, $\Delta E_{\text{p}}$ is the potential energy change of the system, $Q$ is the net energy which is transferred to a system and $W_{\text{s}}$ is the word done by the shaft.

Specific heat capacity $\left(C_p\right)$ of a substance is the amount of heat needed for a unit mass of substance to raise its temperature by $1^{\circ }\text{C}$. It is temperature dependent and varies with temperature of the substance.

Specific enthalpy $\left(\hat{H}\right)$ of any substance at temperature $T^{\circ }\text{C}$ is given by:

$\hat{H}={\int }_{T_{ref}}^T{C}_{p}dT$

             …… (2)

Here, $T_{ref}$ is the reference temperature taken for the calculations.

Kopp’s rule is an empirical method used to determine the specific heat capacity of a solid or liquid substance, as the sum of the heat capacities of each of the atoms present in the molecular formula of the substance.

In Trouton’s rule, entropy of vaporization at normal boiling point is same for most of the liquids which is $\Delta S_v\approx 0.088\text{ kJ/}\left(\text{mol}\cdot \text{K}\right)$. Thus, enthalpy of vaporization at normal boiling point, $T_b{}^{\circ }\text{C}$ is calculated as:

$\Delta H_v=\Delta S_v\left(T_b\right)$

             …… (5)

Interpretation Introduction

(d)

Interpretation:

The rate at which the steam is fed to the reboiler is to be calculated if condensation of saturated steam takes place at $10\text{ bar gauge}$.

Concept introduction:

The rate of heat transfer is calculated as:

$\dot{Q}=\dot{m}\Delta \hat{H}$

             …… (3)