Chapter 4, Problem 4.52P

(a)

Interpretation Introduction

Interpretation:

The value of $\dot{m}\left(\text{steam}\right)/\dot{n}\left(\text{air}\right)$ for the air entering at $1000{}^{\circ }\text{C}$ needs to be determined.

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 is dependent and varies with temperature of the substance. The formula to calculate $C_p$ is:

  $C_p\left(T^{\circ }\text{C}\right)=a+bT+c{T}^2+d{T}^3$ .......(1)

Here, $a,b,c\text{ and }d$ are constants which is specific for a substance.

Change in enthalpy $\left(\widehat{H}\right)$ of any substance from temperature $T_1{}^{\circ }\text{C to }{T}_2{}^{\circ }\text{C}$ is given by:

  $\Delta \widehat{H}={\displaystyle {\int }_{T_1}^{T_2}{C}_{p}dT}$ .......(2)

The rate of heat transfer is calculated as:

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

(b)

Interpretation Introduction

Interpretation:

The value of $\dot{m}\left(\text{steam}\right)/\dot{n}\left(\text{air}\right)$ for the air entering at $500{}^{\circ }\text{C}$ needs to be determined.

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. The formula to calculate $C_p$ is:

  $C_p\left(T^{\circ }\text{C}\right)=a+bT+c{T}^2+d{T}^3$ .......(1)

Here, $a,b,c\text{ and }d$ are constants which is specific for a substance.

Change in enthalpy $\left(\widehat{H}\right)$ of any substance from temperature $T_1{}^{\circ }\text{C to }{T}_2{}^{\circ }\text{C}$ is given by:

  $\Delta \widehat{H}={\displaystyle {\int }_{T_1}^{T_2}{C}_{p}dT}$ .......(2)

The rate of heat transfer is calculated as:

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