Energy required to boil 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.

 

[rwisz]

I would approach this problem by first identifying the variables involved and the relevant equations that can be used to solve for the energy required to boil water. The variables in this problem are the volume of water (3 litres), initial temperature (20 *C), and final temperature (100 *C). The relevant equation for this scenario would be the heat equation, Q = mcΔT, where Q is the energy, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.

To determine the specific heat capacity of water at different temperatures, we can refer to tables or graphs that show the variation of c with temperature. As mentioned in the post, the specific heat capacity of water is not a constant value and does vary with temperature. Therefore, using a constant value for c would not be accurate.

Another factor to consider is the heat of vaporization of water, which is the amount of energy required to change water from liquid to gas at a given temperature. This value is also not constant and can vary with temperature. In order to accurately calculate the energy required to boil water, we would need to use the specific heat capacity and heat of vaporization values at the specific temperatures in question.

In terms of the methods mentioned in the post, both are viable but may not give accurate results. Using the constant specific heat capacity approach may give a rough estimate, but it would not be as accurate as using the specific heat capacity and heat of vaporization values at the specific temperatures. It is also important to double check the units and calculations to ensure accuracy.

In conclusion, the best approach would be to use the heat equation and the specific heat capacity and heat of vaporization values at the specific temperatures to accurately calculate the energy required to boil water. This would provide a more precise answer compared to using constant values or approximations.