Chapter 9, Problem 9.28P

Interpretation Introduction

(a)

Interpretation:

The inlet-outlet enthalpy table for the given process is to be prepared and filled using elemental species as reference. Also, the required heat transfer to the reactor is proven to be $2.7\times {10}^6\text{ kJ}$.

Concept introduction:

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:

$\hat{H}={\int }_{T_{ref}}^T{C}_{p}dT$   .......(1)

Here, $T_{ref}$ is the reference temperature taken for the calculations. And the formula to calculate $C_p$ is:

$C_p=\left(a\times {10}^{-3}\right)+\left(b\times {10}^{-5}\right)T+\left(c\times {10}^{-8}\right)T^2+\left(d\times {10}^{-12}\right)T^3$   .......(2)

The equation for energy balance is:

$\Delta H+\Delta E_{\text{k}}+\Delta E_{\text{p}}=Q-W_{\text{s}}$   .......(3)

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 amount of the energy which is transferred to a system and $W_{\text{s}}$ is the amount of energy which is transferred as shaft work.

Interpretation Introduction

(b)

Interpretation:

The inlet-outlet enthalpy table for the given process is to be prepared and filled using elemental species as reference. Also, the required heat transfer to the reactor is to be calculated.

Concept introduction:

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:

$\hat{H}={\int }_{T_{ref}}^T{C}_{p}dT$   .......(1)

Here, $T_{ref}$ is the reference temperature taken for the calculations. And the formula to calculate $C_p$ is:

$C_p=\left(a\times {10}^{-3}\right)+\left(b\times {10}^{-5}\right)T+\left(c\times {10}^{-8}\right)T^2+\left(d\times {10}^{-12}\right)T^3$   .......(2)

The equation for energy balance is:

$\Delta H+\Delta E_{\text{k}}+\Delta E_{\text{p}}=Q-W_{\text{s}}$   .......(3)

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 amount of the energy which is transferred to a system and $W_{\text{s}}$ is the amount of energy which is transferred as shaft work.

Interpretation Introduction

(c)

Interpretation:

The percentage by which the heat requirement is reduced for the modified process in part (b) is to be calculated. Also, two reasons are to be stated for this reduction along with the benefits of feeding the combustion gas to the calcination reactor.

Concept introduction:

The formula to calculate the percentage reduction is:

$\%\text{ reduction}=\frac{\text{Initial value}-\text{reduced value}}{\text{Initial value}}\times 100\%$   .......(4)