solar domestic hot water
How do you do this question?
Solar energy can preheat cold water for domestic hot-water tanks.
a) What quantity of heat is obtained from solar energy if 100kg of water is preheated from 10 degrees celsius to 45 degrees celsius?
b) If natural gas costs 0.351cents/MJ, calculate the money used if the volume of water in part a) is heated 1500 times per year.
BACKGROUND Definition (skip if you know this):
Heat capacity measures how much heat is needed to change somethings’ temperature. Heat capacity is the amount of heat needed to change the temperature of a unit mass 1°. The heat capacity of water is 1 calorie per gram per degree Celsius (1 cal/g-°C) or 1 British thermal unit per pound per degree Fahrenheit (1 Btu/lb-°F).
See: http://www.answers.com/topic/specific-heat-capacity
(see my more detailed heat-capacity answer: http://answers.yahoo.com/question/index;_ylt=Ai9An5aLmQD74Q0uxYcCJKbsy6IX;_ylv=3?qid=20090204164019AAgaK5U )
How to REASON the answer:
a) energy to raise 100kg water 10 to 45C?
[ 1 calorie = 4.184 J ]
heat capacity of water 1 calorie/gC = 4.184 J/gC
so 4.184 J raises 1g of water, 1 degree Celsius
4,184 J raises 1000g (or 1kg), 1 degree Celsius
418,400 J raises 100,000g (100kg), 1 degree Celsius
[45-10 = 35 ; 35 x 418,400 = 14,644,000]
14,644,000 J raises 100,000g (100kg), 35 Celsius
b) cost of 1500 heatings at 0.351 cents/MJ?
[1 Mega-Joule = 1 Million Joules] (http://www.convert-me.com/en/convert/units/energy/energy.megajoule.en.html)
14.644 MJ x 1500 = 21,966 MJ (per year)
21,966 MJ x 0.351 cents/MJ = 7,710.066 cents
7,710.066 cents x $1/100 cents = $77.10066
so ANSWER
a) 14.644 MJ
b) 7,710.066 cents
for worked examples see:
http://www.sei.ie/Schools/Secondary_Schools/Subjects/Physics/Unit_5_-_Heat_Quantity/Sample_Problems_-_Specific_Heat_Capacities/
http://www.iop.org/activity/education/Projects/Teaching%20Advanced%20Physics/Energy/Thermal%20physics/page_5417.html
http://www.ausetute.com.au/heatcapa.html
Hope this helps.
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