Chapter 8, Problem 8.38P

Interpretation Introduction

(a)

Interpretation:

The final temperature of the air stream 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.

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.

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.

The equation for energy balance is:

$\Delta H+\Delta E_{\text{k}}+\Delta E_{\text{p}}=Q-W_{\text{s}}$   ......(1)

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.

The mole fraction of a species $\left(y_i\right)$ in a mixture is given by:

$y_i=\frac{p_i}{p_{\text{total}}}$   ......(2)

Here, $p_i$ is the partial pressure of the species in the mixture and $p_{\text{total}}$ is the total pressure of the mixture.

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 $22.4\text{ L}$.

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:

$\hat{H}={\int }_{T_{ref}}^T{C}_{p}dT$   ......(3)

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

Interpretation Introduction

(b)

Interpretation:

The rate at which heat is transferred from hot air stream is to be determined.

Concept introduction:

For an adiabatic system, the heat lost by one component in the system is the heat gained by another component in that system. Thus,

$\begin{array}{l}{\dot{Q}}_{lost}={\dot{Q}}_{gain}\\ {\dot{Q}}_{lost}=-\left(\dot{n}{\int }_{T_{ref}}^T{C}_{p}dT\right)\end{array}$   ......(4)

Interpretation Introduction

(c)

Interpretation:

The operation of the spray cooler is to be explained such that a high school senior student can understand.

Concept introduction:

When there is a difference in the temperature of two bodies, then upon the contact of the two system, transfer of heat takes place from higher temperature body to lower temperature body.