# Thermodynaics, solving for minimum power to heat water

1. ### copitlory8

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 10-6 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. ### rock.freak667

6,231
Ok well let's start simple, what equation connects a temperature difference and heat energy?

3. ### SiYuan

27
Power is just the rate at which energy is converted, remember that.

86
Q=cm(deltaT)

5. ### rock.freak667

6,231

And we know that mass = density*volume = ρV and then divide by time, what do we get?

6. ### copitlory8

86
wait i'm getting lost. sorry. so do i do Q=[cpv(deltaT)]/t

7. ### copitlory8

86
so for my answer it would be Power= 4186(1.94)(5E-6)(45.6-15.8) where c=4186 and the density of water is 1.94

8. ### copitlory8

86
is this correct?

9. ### copitlory8

86
oh no wait. i got the density wrong. i have no idea what the density is since the temperature is different

10. ### SiYuan

27
The density of water is 1.94 for feet^3, while your question is in m^3

11. ### copitlory8

86
0.591312 m^3?

12. ### SiYuan

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. ### copitlory8

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. ### SiYuan

27
Your unit conversion is wrong, if you were to use m^3 you should get something else.

15. ### copitlory8

86
Power= 4186(1000)(5E-6)(45.6-15.8)
so the conversion is 1000kg/m^3
is the above formula correct?

16. ### SiYuan

27
It should be right, yes.

17. ### copitlory8

86
thank you so much. i actually learned something for once.

18. ### SiYuan

27
My pleasure, copitlory8

19. ### copitlory8

86
would it be pushing it if i asked you another physics question?

20. ### SiYuan

27
That'd be fine, as long as I can answer it.