Chapter 4, Problem 4.44P

Interpretation Introduction

Interpretation:

Calculate thevolumetric flow rate of fuel gas required to produce carbon dioxide and carbon monoxide after burning with $\text{35\%}$ excess air in a continuous water heater.

Concept Introduction :

The energy balance is applied on continuous water heater to calculate volumetric flow rate. For the energy balance we require the enthalpies of both water entering and leaving and the enthalpy due to the reaction of fuel. So, enthalpies are calculated first. For enthalpy calculation of fuel reaction, composition of product is required which is find by using stoichiometry.

The heat of reaction at any temperature of any reactioncan be calculated as:

  $\Delta H^{\circ }=\Delta H^{\circ }{}_0+R{\displaystyle \underset{T_0}{\overset{T}{\int }}\frac{\Delta C^{\circ }{}_P}{R}dT}$......(1)

Where $\Delta H^{\circ }$ is heat of reaction at any temperature $T$, $\Delta H^{\circ }{}_0$ is heat of reaction at standard temperature $T_0$ .

The standard heat of formation can be calculated as:

  $\Delta H^{\circ }{}_0=\Delta H^{\circ }{}_P-\Delta H^{\circ }{}_R$......(2)

And,

  ${\displaystyle \underset{T_0}{\overset{T}{\int }}\frac{\Delta C^{\circ }{}_P}{R}dT}=(\Delta A)T_0(\tau -1)+\frac{\Delta B}{2}{T}_0{}^2({\tau }^2-1)+\frac{\Delta C}{3}{T}_0{}^3({\tau }^3-1)+\frac{\Delta D}{T_0}(\frac{\tau -1}{\tau })$......(3)

Where $\tau =\frac{T}{T_0}$