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Water heating calculator

This water heating calculator can help you determine both the amount of heat required to raise the temperature of some water (H2O) and the time it will take. It considers the heat capacities of all three states of matter, so it also works if you want to melt the ice or boil water or heat steam.
This calculator uses the latent heat and specific heat constants for water as listed here:

  • The latent heat of fusion is 334 000 J/kg (Energy needed to melt the ice)
  • The latent heat of vaporization is 2 230 000 J/kg (Energy needed to transform liquid water to steam)
  • The specific heat of ice; 2110 J/Kg°C
  • The specific heat of liquid water; 4184 J/Kg°C
  • The specific heat of steam; 2000 J/Kg°C

The fomula used to calculate the needed energy to raise the water temperature a certain number of degrees celsius:
$$Q=mc\Delta T$$
The fomula used when the water goes through transfer, either from ice to liquid water or from liquid to steam:
$$Q=mc$$

…where
m = mass of water (kg)
c = specific or latent heat capacity J/kg
ΔT = Tinitial – Tfinal

If you want to do it manually, here is an example of calculating the amount of heat energy needed to go through two phase changes of water.

Example:
Calculate the energy required to heat a 1kg block of ice at -10 degrees Celsius to a cloud of water vapor at 120 degrees Celsius. Water’s melting point is 0 degrees Celsius and its vaporization point is 100 degrees Celsius at 1 ATM air pressure (sea level).

Step 1: Make a list of known information including the mass of the substance, the phase transition temperatures, the latent heats of fusion and vaporization, the specific heats of each phase of the substance, and the initial and final temperatures of the substance.

We have the following information:

Mass: 1kg
Melting point: 0 °C
Vaporization point: 100°C
Latent heat of fusion: 334 000 J/kg
Latent heat of vaporization: 2 230 000 J/kg
Specific heat of solid phase: 2110 J/Kg°C
Specific heat of liquid phase: 4184 J/Kg°C
Specific heat of gaseous phase: 2000 J/Kg°C
Initial temperature: -10°C
Final temperature: 120°C

Step 2: Calculate the amount of energy required to bring the substance to its first transition temperature using the formula Q=mcΔT.

The ice first needs to heat up to its melting point from -10 degrees C to 0 degrees C, a total temperature change of
$$\Delta T=0-(-10°C)=10°C$$.
Therefore, the total energy required to do this is:
$$Q=mc_s\Delta T=(1,5kg)(2110\frac{J}{kg°C})10°C=31650Joule$$

Step 3: Calculate the energy required to change the substance from its first phase to its second phase using the equation Q=mL.
We can use the latent heat of fusion to calculate the energy required to melt the ice. This will be positive because the ice must take in heat to melt:
$$Q=mL_f=(1,5kg)(334000J/kg)=501 000Joule$$

Step 4: Calculate the energy required to change the temperature of the substance in its second phase to its second transition point using the formula Q=mcΔT.
The liquid water must now be heated to its boiling point from 0 degrees Celsius to 100 degrees Celsius, a total change in temperature of
$$ΔT=100°C -0°C =100°C$$ Then the energy required to heat the water to its boiling point is:
$$mc_l\Delta T=(1,5kg)(4184\frac{J}{kg°C})(100°C)=628500Joule$$

Step 5: Calculate the energy required to change the substance from its second phase to its third phase using the formula Q=mL.
We can use the latent heat of vaporization to calculate the energy change from liquid to gas phase:
$$Q=mL_v=(1,5Kg)(2230000J/kg)=3345000Joule$$

Step 6: Calculate the energy required to change the temperature of the substance in its third phase to its final temperature using the formula Q=mcΔT.
Now we must calculate the energy required to heat steam to its final temperature from its vaporization point, a total change in temperature of
$$ΔT=120°C-100°C=20°C$$ Thus, the energy required to change the steam’s temperature is:
$$Q=mc_g\Delta T=(1,5kg)(2000\frac{J}{kg°C})(20°C)=600000Joule$$

Step 7: Sum the energies calculated in steps 2-6 to calculate the total energy required in the entire process.

The total energy required to change this block of ice into steam at 120 degrees Celsius is:

The total energy required is 4 600 000 joules or if you are doing it on an electric cooking stove is kW/h

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