Chapter 3.9, Problem 16P

(A)

Interpretation Introduction

Interpretation:

The rate of heat must be added to the boiler at a temperature of $300°\text{C}$

Concept Introduction:

The steady state energy balance equation for boiler.

$\frac{d}{dt}\left\{M\left(\widehat{U}+\frac{v^2}{2}+gh\right)\right\}={\dot{m}}_{in}\left({\widehat{H}}_{in}+\frac{v_{in}^2}{2}+g{h}_{in}\right)-{\dot{m}}_{out}\left({\widehat{H}}_{out}+\frac{v_{out}^2}{2}+g{h}_{out}\right)+{\dot{W}}_S+{\dot{W}}_{EC}+\dot{Q}$

Here, mass flow rate for inlet and outlet is ${\dot{m}}_{in}$ and ${\dot{m}}_{out}$, specific enthalpies of inlet and outlet is ${\widehat{H}}_i$ and ${\widehat{H}}_{out}$, heights at which streams enters and leave the system is $h_{in}$ and $h_{out}$, time taken is t, mass of the system is M, specific internal energy is $\widehat{U}$, velocity is v, height is h, acceleration due to gravity is g, rate at which work is added to the system is ${\dot{W}}_{EC}$, rate of shaft work is ${\dot{W}}_S$, and the rate of heat addition to the system is $\dot{Q}$.

The steady state mass balance equation for heat exchangers.

$0={\dot{m}}_{in,1}+{\dot{m}}_{in,2}+{\dot{m}}_{in,3}-{\dot{m}}_{out}$

Here, inlet mass flow rate for state 1, 2, and 3 is ${\dot{m}}_{in,1},{\dot{m}}_{in,2},and{\dot{m}}_{in,3}$ respectively.

(B)

Interpretation Introduction

Interpretation:

The temperature of the exiting steam.

Concept Introduction:

Write the formula of interpolation method of two variables.

$y_2=\frac{\left(x_2-x_1\right)\left(y_3-y_1\right)}{\left(x_3-x_1\right)}+y_1$

Here, the variables denoted by x and y are enthalpy and temperature.