You decide to generate steam to drive a series of radiators

You decide to generate steam to drive a series of radiators in your home to stay warm and save on power. In your frustration, you decide to burn your engineering textbooks and generate 50kW of power. At chemical engineering friend designed a heat exchanger for you and half of the power from burning of the books can be transferred as heat via the heat exchanger. When you burn your textbooks they produce stack gases at 451 degree F at atmospheric pressure. The combustion products are vented to the atmosphere. Saturated water enters the heat exchanger at 25 degree C and leaves as saturated steam at 218 PSl absolute. Use one sentence to state why the ideal gas law applies, or does not apply, to this system. Calculate the rate of steam produced in kg/hr. Calculate the volume of steam produced in m^3/hr.

Solution

a)

Since there is phase change happening from liquid water to vapor, we cannot apply ideal gas law.

b)

Power input to heat exch = Half of 50 kW = 25 kW = 1421.7 Btu/min

From steam tables, at 218 psi we get h_vap = 1200 Btu/lb, h_liq = 363 Btu/lb

1421.7 = m*(h_vap - h_liq)

1421.7 = m*(1200 - 363)

m = 1.7 lb/min

= 0.77 kg/min

= 46.2 kg/hr

c)

From steam tables, at 218 psi we get v_vap = 0.475 ft3 / lb

V = m*v_vap

= 1.7*0.475

= 0.8075 ft3 / min

= 1.372 m³ / hr