Thermodynaics, solving for minimum power to heat water

copitlory8

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.

rock.freak667

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

SiYuan

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

copitlory8

Q=cm(deltaT)

rock.freak667

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

copitlory8

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

copitlory8

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

copitlory8

is this correct?

copitlory8

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

SiYuan

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

copitlory8

0.591312 m^3?

SiYuan

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.

copitlory8

yeah. 1.94 is ft^3

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

SiYuan

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

copitlory8

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

SiYuan

It should be right, yes.

copitlory8

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