Calculating Time for Immersion Heater to Raise Water Temperature

[physicskillsme]

Extracted from another thread tha had got a bit messy.

The immersion heater in an electric hot water system is rated at 9 kW. If the tank is initially filled with 40 gallons (about 150 litres, with a mass of 150 kg) of cold water at 15 oC, how long will it take the heater to raise the temperature to 40 oC?

Ok this is as far as I have got:

Q=CmdeltaT

deltaT=40-15 = 25

q=Q=4196*150*25

15735000J

Ok so now I need to get time.

p=deltaq/deltat

So to get time do I just say time=p*delta q ?

 

[Hootenanny]

So to get time do I just say time=p*delta q ?

Almost but not quite, i think you algerbraic skills are letting you down;

$$P = \frac{\Delta Q}{\Delta t}$$

$$P\Delta t = \Delta Q$$

$$\Delta t = \frac{\Delta Q}{P}$$

Your theory is right, just the manipulation. A quick check to see if your manipulation is right is to take a look at the units.

-Hoot

 

[physicskillsme]

Almost but not quite, i think you algerbraic skills are letting you down;

$$P = \frac{\Delta Q}{\Delta t}$$

$$P\Delta t = \Delta Q$$

$$\Delta t = \frac{\Delta Q}{P}$$

Your theory is right, just the manipulation. A quick check to see if your manipulation is right is to take a look at the units.

-Hoot

So I need to do the calcualtions for each of these steps?

Yes I am having problems with solving for variables it just seems so complicated. Do you know of any good tutorials for this?

 

[Hootenanny]

So I need to do the calcualtions for each of these steps?

No, all you have done is re-arranged an equation, you can just plug your numbers in for P and $\Delta Q$(which you have calculated earlier).

Do you know of any good tutorials for this?

I'm afraid I don't, but a quick internet search would probably show up a few. If you can get hold of a high school mathematics textbook, that would probably be best.

-Hoot

 

[physicskillsme]

So this the solution?

The immersion heater in an electric hot water system is rated at 9 kW. If the tank is initially filled with 40 gallons (about 150 litres, with a mass of 150 kg) of cold water at 15 oC, how long will it take the heater to raise the temperature to 40 oC?

Q=CmdeltaT

deltaT=40-15 = 25

Q=4196*150*25

15735000J

delta t= delta q/p

1748.33 =15735000/9000

1748 seconds

 

[Hootenanny]

Yep, that looks right to me

-Hoot