# How to calculate the heat of vaporization

## Internal energy - heat capacity

#### Specific heat of fusion and evaporation of ice or water

Note: Heat of fusion and heat of evaporation are sometimes also referred to as melting energy and energy of evaporation. For \ (1 \, \ rm {kg} \) water the important energies are given in the following diagram.

The diagram shows that evaporation energy and condensation energy or melting energy and solidification energy are equal.

#### The energy required and energy released during phase transitions are the same

So if you cool a gas, it will condense at the condensation temperature. Energy is released when it condenses. The same energy is required to vaporize the substance again. The condensation energy is equal to the evaporation energy.
If you cool a liquid, it solidifies at the solidification temperature. When solidifying, energy is also released. The same energy is required to melt the substance again. The solidification energy is equal to the melting energy.

In general

• At transitions where the bond between the particles loosens, energy has to be added (solid-> liquid, liquid-> gaseous, solid-> gaseous).
• At transitions where the bond between the particles becomes stronger, energy is released (gaseous-> liquid, liquid-> solid, gaseous-> solid).

Note: The heat of fusion and evaporation of water is relatively large. The energy that you have to use to melt \ (1 \, \ rm {kg} \) ice corresponds to the energy that is necessary to \ (1 \, \ rm {kg} \) water from \ ( 0 ^ \ circ {\ rm {C}} \) to about \ (80 ^ \ circ {\ rm {C}} \).

#### Specific heat of fusion and evaporation

If you want to calculate how much energy is necessary to heat a pure solid, a pure liquid or a pure gas (without phase transition!), One uses the relation: \ [\ Delta E _ {\ rm {i}} = c \ cdot m \ cdot \ Delta \ vartheta. \] The specific heat capacity of solid, liquid or gas is to be used for \ (c \).

To calculate how much energy has to be used for melting or evaporation, you can use the following relationships: \ [\ Delta E _ {\ rm i} = s \ cdot m \ qquad \ rm {or} \ qquad \ Delta E_ {\ rm i} = r \ cdot m \] Here \ (s \) and \ (r \) each represent the specific heat of fusion or evaporation. Their unit is \ (\ rm {\ frac {J} { g}} \) (or \ (\ rm {\ frac {kJ} {g}} \)).

You can find an experiment to determine the heat of fusion here. An attempt to determine the heat of vaporization here.

A list of table values ​​for specific melting and evaporation energies can be found at Wikipedia: List of melting energies; List of evaporation energies