Chapter 8, Problem 8.57P

Interpretation Introduction

(a)

Interpretation:

The degree-of-freedom analysis for the given process is to be done to prove that the information given is sufficient to calculate the cooling duty of the air conditioner.

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.

Degree of freedom analysis is the procedure to analyze any missing information needed for material balance calculations. The procedure involves complete labelling of the flowchart representing the process and then determining number of unknown variables $\left(n_{\text{unknowns}}\right)$ and independent equations $\left(n_{\text{indep eqns}\text{.}}\right)$ from that flowchart.

Mathematically, degree of freedom $\left(n_{\text{df}}\right)$ is formulated as:

$n_{\text{df}}=n_{\text{unknowns}}-n_{\text{indep eqns}\text{.}}$ ...… (1)

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:

The rate of condensation of water and cooling duty in tons for the air conditioner are to be determined.

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:

$\Delta H+\Delta E_{\text{k}}+\Delta E_{\text{p}}=Q-W_{\text{s}}$ ...… (2)

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:

$y_i=\frac{p_i}{p_{\text{total}}}$ ...… (3)

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

The formula to calculate relative humidity is:

$h_r=100\times \frac{p_{{\text{H}}_2\text{O}}}{p_{{\text{H}}_2\text{O}}{}^{\ast }\left(T\right)}$ ...… (4)

Here, $p_{{\text{H}}_2\text{O}}$ is the partial pressure of ${\text{H}}_2\text{O}$ and $p_{{\text{H}}_2\text{O}}{}^{\ast }\left(T\right)$ is the equilibrium pressure of ${\text{H}}_2\text{O}$ at temperature $T$.

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 $22.4\text{ L}$.