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Thermodynaics, solving for minimum power to heat water 
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#1
Sep1910, 02:17 PM

P: 86

An electric hot water heater takes in cold water at 15.8°C and delivers hot water. The hot water has a constant temperature of 45.6°C, when the "hot" faucet is left open all the time and the volume flow rate is 5.0 multiplied by 106 m3/s. What is the minimum power rating of the hot water heater?
I really need help. I don't know how to connect Power and Thermal Energy. I know the individual formulas but can't connect the two. This is for WebAssign and is due within the hour. Please provide quick solution. Thank you very much. 


#2
Sep1910, 02:19 PM

HW Helper
P: 6,202




#3
Sep1910, 02:21 PM

P: 27

Power is just the rate at which energy is converted, remember that.



#4
Sep1910, 02:23 PM

P: 86

Thermodynaics, solving for minimum power to heat water
Q=cm(deltaT)



#5
Sep1910, 02:28 PM

HW Helper
P: 6,202




#6
Sep1910, 02:41 PM

P: 86

wait i'm getting lost. sorry. so do i do Q=[cpv(deltaT)]/t



#7
Sep1910, 02:46 PM

P: 86

so for my answer it would be Power= 4186(1.94)(5E6)(45.615.8) where c=4186 and the density of water is 1.94



#8
Sep1910, 02:46 PM

P: 86

is this correct?



#9
Sep1910, 02:48 PM

P: 86

oh no wait. i got the density wrong. i have no idea what the density is since the temperature is different



#10
Sep1910, 02:53 PM

P: 27




#11
Sep1910, 03:11 PM

P: 86

0.591312 m^3?



#12
Sep1910, 03:13 PM

P: 27

The average density of water should be 1g/ml, or 1g/cm^3,
whilst 1.94 is for lb/ft^3 if I recall right. 


#13
Sep1910, 03:23 PM

P: 86

yeah. 1.94 is ft^3
so in the equation i would actually plug in .001kg/m^3 since were using kg not g 


#14
Sep1910, 03:24 PM

P: 27

Your unit conversion is wrong, if you were to use m^3 you should get something else.



#15
Sep1910, 03:28 PM

P: 86

Power= 4186(1000)(5E6)(45.615.8)
so the conversion is 1000kg/m^3 is the above formula correct? 


#16
Sep1910, 03:31 PM

P: 27

It should be right, yes.



#17
Sep1910, 03:35 PM

P: 86

thank you so much. i actually learned something for once.



#18
Sep1910, 03:35 PM

P: 27

My pleasure, copitlory8



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