Work out how long it takes to warm up water

robert jr · #1 $Old$ October 22nd, 2008, 12:40 PM

Hello,

I'm trying so very hard to work out how long it will take to warm up 5 liters of water.

500 watt heating element
Battery = 12V power, 40 Amps

Amount of water = 5 liters
Final Temp = 65 degrees
Ambient Temp = 45 degrees

Ive worked out that it takes 41.86 K joules to heat the required water, so how do i then work out how long it will take to heat up using the specified equipment?

Thanks in advanced!

Rob

Opalg · #2 $Old$ October 22nd, 2008, 01:56 PM

Quote:

Originally Posted by robert jr $View Post$

500 watt heating element
Battery = 12V power, 40 Amps

Amount of water = 5 liters
Final Temp = 65 degrees
Ambient Temp = 45 degrees

Ive worked out that it takes 41.86 K joules to heat the required water, so how do i then work out how long it will take to heat up using the specified equipment?

1 watt is 1 joule per second. The heating element is rated at 500 watts, but the battery can only deliver 12×40 = 480 watts, so I assume that that is all that is available for heating. If the figure of 41.86 kJ is correct then the time taken for the heating element to deliver this amount of energy will be $\frac{41.86\times10^3}{480}$ seconds. (That's a bit less than one and a half minutes, which sounds a bit fast to heat up that amount of water. But we are assuming that no energy is lost, and that the entire 480 watts goes into heating the water.)

robert jr · #3 $Old$ October 22nd, 2008, 02:28 PM

thanks! yeh it seems a little to quick, it turns out that it actually takes 1750082.4 J to heat the water. so it would take 59 mins??

im confused

Opalg · #4 $Old$ October 22nd, 2008, 02:50 PM

I believe that if you heat 1 gramme of water by 1 degree celsius you will use 4.2 joules. So to heat 5 litres = 5000 grammes through 20° should take about 5000×20×4.2 = 420,000 joules.

robert jr · #5 $Old$ October 22nd, 2008, 03:00 PM

thanks,

i understand now