Immersion heater probelm

1. Mar 30, 2006

physicskillsme

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 ???

2. Mar 30, 2006

Hootenanny

Staff Emeritus
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

3. Mar 30, 2006

physicskillsme

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?

4. Mar 30, 2006

Hootenanny

Staff Emeritus
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).

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

5. Apr 3, 2006

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

6. Apr 3, 2006

Hootenanny

Staff Emeritus
Yep, that looks right to me

-Hoot