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Physics heat question?

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a hot water heater is operated by solar...if the solar heater has an area of 6.0m^2 and the power delivered by sunlight is 550 W/m^2, how long will it take to increase the temp of 1 m^3 of water from 20 to 60 C?

i know the formula Q=mcdeltaT but i don't understand the reasoning behind how to find how much time it will take?

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  1. In the formula Q=m*C*∆T, you need to understand not only what every variable means, but also the units.  It'll help you understand.

    m is obviously mass, which is in kilograms.  Ã¢ÂˆÂ†T is the change in temperature, which in this case is (60-20)C, which is 40C.  C is the specific heat of water, which is 4186 J/(kg*C) [Joules per kilogram degree Celsius].  Q is the heat energy which is in Joules.

    You have everything to solve for Q except for mass, which you get from the volume of water (1 m^3) and the density of water (1000kg/m^3).

    m = density*volume = (1000kg/m^3)*(1m^3) = 1000kg

    Everything for Q is known, and so Q can be solved for...

    Q = (1000 kg)*(4186 J/kgC)*(40C) = 167440000 J = 167.44 MJ [Mega Joules]

    It is now important to know what a Watt is.  A Watt is the unit of power, which is an amount of energy per unit time, in this case Joules per second.  The total power is found by multiplying the power delivered by the sunlight by the area...

    P = (6.0 m^2)*(550 W/m^2) = 3300 W = 3300 J/s

    The needed energy is 167.44 MJ, which is equal to the delivered power multiplied by time ( E = P*t  --> t = E/P).  Time can be found...

    t = (167440000 J)/(3300 J/s) = 50,739.4 seconds = 845.66 minutes = 14.09 hours = 14 hours 5.4 minutes

    I hope that answered the question.  If my actual number answer is wrong, then I don't know what happened.  I do know that the method, however, is correct.


  2. 40=x+13.75

    40-13.75=x

    26.25minutes


  3. The above answer is good; I was trying to answer that last night when Yahoo! answers went down for maintenance and couldn't answer you! Anyway, I made .pdf for you if you still need it. I'm sure it says the same thing the Ryan says, but maybe in a slightly different way if you'd like two points of view.
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