Chapter 8, Problem 8.48P

Interpretation Introduction

(a)

Interpretation:

The rate of heat removal from the adsorber is to be calculated such that the process remains isothermal. Also, the time taken to reach the saturation of bed is to be calculated.

Concept introduction:

When vapor from a gas mixture is transferred to a solid surface, gas adsorption occurs. It can be treated as condensation of vapor on a solid surface in a simplified way.

Raoult’s law states that,

$x_{\text{A}}{P}_{\text{A}}{}^{\ast }=y_{\text{A}}P$ .......(1)

Here, $x_{\text{A}}$ is the mole fraction of A in liquid phase, $P_{\text{A}}{}^{\ast }$ is the vapor pressure of A, $y_{\text{A}}$ is the mole fraction of A and $P$ is the total pressure of the system.

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

${\log }_{10}{P}^{\ast }=A-\frac{B}{T+C}$ .......(2)

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

The rate of heat transfer is calculated as:

$\dot{Q}=\dot{n}\Delta \hat{H}$ .......(3)

Removal of heat from any vapor at its normal boiling point leads to the condensation of the vapor to liquid phase until all the vapor is condensed and further removal of heat leads to the cooling of the liquid. If less heat is removed from the vapor, then partial condensation happens, and vapor and liquid coexist at its normal boiling point.

Interpretation Introduction

(b)

Interpretation:

The formula for surface-to-volume ratio for the spherical particles is to be derived. Based on this formula, the efficiency of the adsorption process on decreasing the particle average diameter is to be explained. Also, the irrelevance of calculating the surface-to-volume formula is to be explained.

Concept introduction:

When vapor from a gas mixture is transferred to a solid surface, gas adsorption occurs. It can be treated as condensation of vapor on a solid surface in a simplified way.

Volume of a sphere $\left(V_s\right)$ is given by:

$V_s=\frac{4}{3}\pi r^3$ .......(4)

Here, $r$ is the radius of the sphere in $\text{'}\text{cm}\text{'}$.

Surface area of a sphere $\left(S{A}_s\right)$ is given by:

$S{A}_s=4\pi r^2$ .......(5)

Here, $r$ is the radius of the sphere in $\text{'}\text{cm}\text{'}$.