Question

Reserve Problem 4.006 Tutorial SI

Answer 1

Answer:

a) $T = 151.83^{\textdegree}C$, b) $\dot m_{2} = 58.61\times 10^{3}\,\frac{kg}{h}$

Explanation:

A feedwater heater is a mixing chamber that pre-heats water prior to compressor, improving the efficiency of the power cycle. This system is modelled after the First Law of Thermodynamics:

$\dot m_{1}\cdot h_{1} + \dot m_{2}\cdot h_{2} - (\dot m_{1}+ \dot m_{2})\cdot h_{3} = 0$

The properties at inlets and outlets are, respectively:

Inlet 1 (Subcooled Liquid)

$h_{1} = 188.44\,\frac{kJ}{kg}$

Inlet 2 (Superheated Vapor)

$h_{2} = 3106\,\frac{kJ}{kg}$

Outlet 3 (Saturated Liquid)

$h_{3} = 640.09\,\frac{kJ}{kg}$

a) The temperature at the exit is:

$T = 151.83^{\textdegree}C$

b) The mass flow rate at inlet 2 is:

$\left(3.2\times 10^{5}\,\frac{kg}{h} \right)\cdot \left(188.44\,\frac{kJ}{kg} \right) + \dot m_{2}\cdot \left(3106\,\frac{kJ}{kg} \right) - \left(3.2\times 10^{5}\,\frac{kg}{h}+\dot m_{2}\right)\cdot \left(640.09\,\frac{kJ}{kg} \right)= 0$$2465.91\cdot \dot m_{2} -144528000 = 0$

$\dot m_{2} = 58.61\times 10^{3}\,\frac{kg}{h}$