# How long to heat 50 liters of water at 20 degrees Celsius to 60 degrees Celsius with 5400 watts?

To answer this one need to know the specific heat capacity of water, which is usually quoted as 4.2 J/kg/K. It's not actually a constant, but from 20 to 60 degrees at atospheric pressure, it's good enough.

So 4.2 J/kg/K.

K first. 60 deg - 20 deg = 40 deg difference. The increments of degrees and kelvins are the same, so that's also 40 K.

Now kg. 50 litres is a lot of water. Not coincidentally, 1l has a mass of 1kg. So 50kg.

4.2J? Well we can pump is 5400 W, which is 5400 J/s.

Now the maths...

4.2 J/kg/K... we have 50 kg

50 kg * 4.2 J/kg/K = 210 J/K

210 J/k... OK, but we have 40 of them kelvin things...

210 J/K * 40 K = 8400 J

8400 J.... and we have 5400 J/s at our disposal

8400 J / 5400 J/s = 1.6s

1.6 s

Pretty quick. In real life you'd be hard pressed to come close
to this. You'd expect some inefficiencies. Time how long it takes
for your kettle to boil one litre of water and then see how long it
should have taken using the power rating on the base of the kettle.
Without looking at *your* kettle, maybe double?

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