How Much Energy Does It Take to Boil 3 Liters of Water?

[northh]

1. Problem, data and attempt at a solution

How much energy is required to boil off 3 litres of water from 20*C?

This is not really homework, but I still thought this would be the best place to post:
To get something to compare to in terms of energy (joule/watt), I would like to know approximately how much energy it takes to boil all the water in a standard kettle (3 litres).

I tried doing this with data from log p H (mollier) diagrams for water:
Enthalpy of water at 20 *C and athmospheric pressure from mollier: 86,6 kJ/kg
Enthalpy of saturated steam (100*C): 2676,1 kJ/kg
DeltaH= 2676,1 - 86,6 = 2589,5 kJ/kg
3 litres of water = 3kg so: 2589,5 kJ/kg * 3 kg = 7768,5 kJ required to boil 3 litres of water.

However when searching for this on google i only found another solution to the problem that did not match my answer using constant specific heat capacity and heat of vaporization:

http://wiki.answers.com/Q/How_much_energy_is_needed_to_boil_water#ixzz18El72mGe

However according to wikipedia: "The specific heat capacities of substances comprising molecules (as distinct from monatomic gases) are not fixed constants and vary somewhat depending on temperature."

So using a constant heat capacity value from 20 *C to 100 *C would be wrong, no?

Are any of these methods viable? Which is better? They don't match up when i use his equation for my case (although I know it's partly because we have different values for heat of vaporization and it seems like he has mixed up some units in his description).

 

[gneill]

The specific heat of liquid water changes with temperature, but not by too much. At 20C it's 4.183 (kJ/kg/K), while at the boiling point it's 4.219. If you need great accuracy you could fit a curve and run the numbers step by step (computers are handy things).

 

[northh]

Ok, I've been looking at some tables to find a constant to use. They vary greatly. Here is even one from wikipedia where the specific hc is constant but the volumetric varies with temperature:

Water at 25 °C liquid: 4.1813 J/g*K - 4.1796 J/cm3*K
Water at 100 °C liquid: 4.1813 J/g*K - 4.2160 J/cm3*K

source: http://en.wikipedia.org/wiki/Specific_heat

Surely this must be wrong, as 1 cm3 = 1 g for water (density 1000 kg/m3)?

 

[gneill]

Ok, I've been looking at some tables to find a constant to use. They vary greatly. Here is even one from wikipedia where the specific hc is constant but the volumetric varies with temperature:

Water at 25 °C liquid: 4.1813 J/g*K - 4.1796 J/cm3*K
Water at 100 °C liquid: 4.1813 J/g*K - 4.2160 J/cm3*K

source: http://en.wikipedia.org/wiki/Specific_heat

Surely this must be wrong, as 1 cm3 = 1 g for water (density 1000 kg/m3)?

Water changes density with temperature. In fact, it's got an 'abnormal' density versus temperature curve compared to other substances, particularly near the freezing point.