Chapter 8, Problem 8.64P

Interpretation Introduction

(a)

Interpretation:

The feed ratio $\left(\text{L dry air}\left(\text{STP}\right)/\text{ kg dry film}\right)$ for the process is to be determined.

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.

Antoine equation is used to determine the vapor pressure of any substance at the given temperature by the equation:

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$ ...… (1)

Here, $A,B\text{ and }C$ are the constants specific for a substance given in table B.4 of appendix B.

For two phase binary mixture, Raoult’s law states that,

$\begin{array}{c}{x}_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P\\ x_{\text{B}}{P}_{\text{B}}{}^{\ast }=y_{\text{B}}P\end{array}$ ...… (2)

Here, $x_{\text{A}}\text{ and }{x}_{\text{B}}$ are the mole fractions of A and B in liquid phase respectively, $P_{\text{A}}{}^{\ast }\text{ and }{P}_{\text{B}}{}^{\ast }$ are the vapor pressure of A and B respectively, $y_{\text{A}}\text{ and }{y}_{\text{B}}$ are the mole fractions of A and B respectively and $P$ is the total pressure of the system.

An ideal gas is the gas which obeys ideal gas laws which is a simplified equation of states.

A real gas behaves as an ideal gas at higher temperature and lower pressure. At STP, a mole of an ideal gas has a volume of $22.4\text{ L}$.

Interpretation Introduction

(b)

Interpretation:

An expression for $T_{\text{a1}}$ in terms of the film temperature change, $\left(T_{\text{f2}}-35\right)$, is to be derived.

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:

$\text{input+generation-output-consumpumtion=accumulation}$

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:

$\Delta \dot{H}+\Delta {\dot{E}}_{\text{k}}+\Delta {\dot{E}}_{\text{p}}=\dot{Q}-{\dot{W}}_{\text{s}}$ ...… (5)

Here, $\Delta \dot{H}$ is the rate of change in the enthalpy of the system, $\Delta {\dot{E}}_{\text{k}}$ is the rate of kinetic energy change of the system, $\Delta {\dot{E}}_{\text{p}}$ is the rate of potential energy change of the system, $\dot{Q}$ is the net rate at which energy is transferred to a system and ${\dot{W}}_{\text{s}}$ is the rate at which energy is transferred as shaft work.

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:

$\hat{H}={\int }_{T_{ref}}^T{C}_{p}dT$ ...… (6)

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

Interpretation Introduction

(c)

Interpretation:

The film temperature change is to be calculated is the inlet temperature of the air is ${120}^{\circ }\text{C}$.

Interpretation Introduction

(d)

Interpretation:

The required value of $T_{\text{a1}}$ is to be calculated if the film temperature falls to ${34}^{\circ }\text{C}$ and if it rises to ${36}^{\circ }\text{C}$.

Interpretation Introduction

(e)

Interpretation:

The reason for the decrease in the temperature of the film is to be explained even if the temperature of the inlet air is kept higher than the inlet film temperature.

Concept introduction:

In an adiabatic system, when evaporation takes place, the heat from the condensate is used to evaporate the volatile liquid after all the heat from the air is used up.