5.4 The following problem illustrates the power of the 1s law in making crude ba
ID: 2074748 • Letter: 5
Question
5.4 The following problem illustrates the power of the 1s law in making crude back of the envelope calculations to predict the performance for a diversity of engineering systems. These tools are useful early on in a design process when evaluating a variety of technical options. A hint for this problem, don 't forget the incompressible substance model when working with substances in the liquid or solid phase During the day, a home is heated passively by solar radiation. Passive solar heaters can be used to store this energy from radiation. Let's say a home stores 500 x 2L transparent plastic bottles filled with water, and these bottles are in direct contact with solar radiation (positioned near a window). During the day the water in these bottles reach a temperature of 170°F. At night, a temperature controlled natural gas boiler turns on once the temperature of the house drops below 68 . The boiler delivers heat at a rate of 55,000 BTU/h. Assume the home is maintained at 68 °F, and loses heat to the surroundings at an average rate of 50,000 BTU/h. Determine a) how long the boiler was operating with the thermal energy storage (i.e. plastic bottles), and b) how long the boiler operates without the heat storage. Use the full Give/Find/Models/Solve method. Reflect on the difference in your answer in part a vs. part b.Explanation / Answer
q = m cp dT / t .
q = mean heat transfer rate (Btu/hr))------55000 Btu/Hr
m = mass of the product (Ib)-----2204.62 Ib
cp = specific heat of the product (BTU/(Ib F)) -----1.002 (BTU/(Ib F))
dT = Change in temperature of the fluid (F)----(170-68) F
t = total time over which the heating process occurs (HR)
So,'
q=MCpdT/time
Time=2204.62*1.002*(170-68)/55000
Time=4.096 Hr.
Boiler Work with Thermal Energy Storage i.e Time required 4.096 hr.
II.
Boiler heat rate=55000 Btu/Hr.
Specfic Entalphy of Water @ 170 Deg F=142 btu/Ib.
Specfic Entalphy of Water @ 68 Deg F=32 btu/Ib.
Heat Out Put= (Specfic Entalpy @ 170 F-Spefcic Entalphy @ 68 f)*55000
Heat Out Put=6050000 Btu/Hr.
Boiler Eff=0.80.
Heat Input =Heat Out Put /Eff
= 6050000/.8
= 7562500 Btu/Hr.
NCV of Natural Gas=22446 Btu /Ib.
Fuel Consuption Rate= 7562500/(22446)
= 337 IB/Hr
Water Bottle wt is 2205 IB.
So, With out Water Bottle =2205/337
=6.54 Hr.
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