# Heat of evaporation

The heat of evaporation ΔQ v is the heat that is required to evaporate a certain amount of a liquid, i.e. to transfer it from the liquid to the gaseous state of aggregation . In the case of condensation , which is the reverse of evaporation, the same amount of heat is released again as heat of condensation . The heat of evaporation is an important parameter in the vapor pressure curve . Technically, the heat of vaporization for cooling applied .

## Severing work

For the transition from the liquid to the gaseous aggregate state - even if the liquid is already at the boiling point - energy must be supplied. This separation work serves to overcome the forces of attraction between the liquid particles . Due to the law of conservation of energy , the applied energy is not lost, but becomes part of the internal energy U contained in the gas .

The separation work is smallest with liquefied noble gases , since only Van der Waals forces have to be overcome, with other liquids dipole moments or hydrogen bonds are added. The heat of evaporation is even higher with metals (strong metallic bond ) and highest with salts because of the comparatively extremely strong ionic bond .

Change of equilibrium using the example of water

Example: In order to evaporate one kilogram of water at 100 ° C and 1013 mbar, the separation work ΔU = 2088 kJ has to be used. The separation work for water is relatively high because of the hydrogen bonds between the water molecules.

## Work of displacement in the isobaric case

In addition, the amount of heat of evaporation to be supplied depends on the process conditions. If the evaporation or evaporation takes place isobarically at constant pressure p , as is often the case, then the gas produced must, in order to expand from the liquid volume V F to the gas volume V G , against the external pressure p the displacement work p (V G - V F ) = p ΔV . The energy supplied is therefore used both for the separation work and for the displacement work: ΔQ v = ΔU + p · ΔV .

Example: At 100 ° C and 1013 mbar, one kilogram of water has a volume of 1.04 dm 3 in the liquid state and a volume of 1.673 m 3 in the gaseous state . The water concentration in the gas phase is then 598 g / m³ at 100 ° C (see vapor pressure curve ).

The
amount of saturation of water vapor in air as a function of temperature .

The increase in volume during evaporation is therefore 1.672 m 3 and the work of displacement performed during expansion against the external air pressure is 169 kJ. The heat of evaporation to be supplied under isobaric conditions at 100 ° C. and 1013 mbar per kg of water is therefore ΔQ v = ΔU + p · ΔV = 2088 kJ + 169 kJ = 2257 kJ = 2.26 MJ.

Under other conditions, such as B. evaporation in a vacuum, evaporation at constant volume, etc. different laws apply.

## Heat of evaporation and enthalpy of evaporation

State and process variables :
Enthalpy H , enthalpy of evaporation ΔH V
Pressure p , liquid volume V F , gas volume V G
Work of displacement (W =) p ΔV , work of volume change W v
Internal energy U   (separation work ΔU ), heat of evaporation (supplied energy) ΔQ v

The state variable formed from the state variables , and${\ displaystyle U}$${\ displaystyle p}$${\ displaystyle V}$

${\ displaystyle H = U + p \ cdot V}$

is called enthalpy . Change , and by the amounts , and , so change by the amount ${\ displaystyle U}$${\ displaystyle p}$${\ displaystyle V}$${\ displaystyle \ Delta U}$${\ displaystyle \ Delta p}$${\ displaystyle \ Delta V}$${\ displaystyle H}$

${\ displaystyle \ Delta H = \ Delta U + V \ cdot \ Delta p + p \ cdot \ Delta V}$.

If the pressure remains constant, as in the case under consideration, then is

${\ displaystyle \ Delta H = \ Delta U + p \ cdot \ Delta V}$.

In this isobaric case is the energy supplied and distributed over the work of separation and displacement

${\ displaystyle \ Delta Q_ {v} = \ Delta U + p \ cdot \ Delta V}$

thus equal to the change in enthalpy of the system

${\ displaystyle \ Delta Q_ {v} = \ Delta U + p \ cdot \ Delta V = \ Delta H_ {v}}$

and is then also called enthalpy of evaporation . ${\ displaystyle \ Delta H_ {v}}$

Example: the enthalpy of vaporization of 1 kg of water is 2257 kJ (at 100 ° C).

The use of the symbol emphasizes that the energy is supplied in the form of heat, the use of the symbol emphasizes that the state variable enthalpy of the system is changed. ${\ displaystyle \ Delta Q_ {v}}$${\ displaystyle \ Delta H_ {v}}$

Numerous everyday evaporation and evaporation processes take place under isobaric conditions because the systems concerned are exposed to atmospheric air pressure. The evaporation heat to be expended is then in particular an evaporation enthalpy and is tabulated under this name for many substances.

The substance-specific enthalpy of vaporization depends on the temperature, but not on the external air pressure. Tabular values ​​are usually found for the boiling point of the substance (vapor pressure of the substance is then 1013 mbar). The specific heat of vaporization relates to 1 kg (or 1 g), the enthalpy of vaporization to 1 mol of the evaporating substance.

For any temperature, the molar enthalpy of vaporization can be calculated from the measured vapor pressure (of the substance to be distilled) using the Clausius-Clapeyron relationship ( saturation vapor pressure ).

Calculated enthalpy of evaporation temperatures for water

Temperature
in
° C

Enthalpy of evaporation in
kJ mol −1
comment
000 45.054
025th 43,990 "Standard enthalpy of vaporization"
040 43,350
060 42,482
080 41,585
100 40.657 Normal boiling point = 2.26 MJ / kg water
120 39.684 all measurements> 100 ° C with compressed water vapor
140 38.643
160 37.518
180 36,304 about 10 bar steam
200 34.962
220 33,468
240 31.809
260 29,930
280 27.795
300 25,300
320 22.297
340 18.502
360 12.966
374 02.067 approximately critical temperature

The molar enthalpy of vaporization (in kJ / mol) can be converted into the specific enthalpy of vaporization (in kJ / g) by dividing it by the molar mass (here: 18.02 g / mol for water).

The molar enthalpy of vaporization of water can be calculated in the temperature range from 273 to 473 K (0 to 200 ° C) using the following empirical formula:

${\ displaystyle H_ {v} = \ left (50 {,} 09-0 {,} 9298 \ cdot {\ frac {T} {1000}} - 65 {,} 19 \ cdot \ left ({\ frac {T } {1000}} \ right) ^ {2} \ right) \ mathrm {\ frac {kJ} {mol}}.}$

## Heat of condensation

If the gas condenses again under the same conditions, the evaporation heat used for evaporation is also released again in the form of the identical amount of heat of condensation . One then clearly speaks of the fact that this energy was stored in the gas in the form of imperceptible latent heat . However, this is not always thermal energy . Instead, the heat of evaporation during evaporation is partly converted into internal energy in technical processes and partly given off to the environment as mechanical work.

## Heat of sublimation

In the case of sublimation ( phase change from solid to gaseous) one speaks of sublimation heat , which in addition to the heat of evaporation also includes the heat of fusion of the substance. Water can also sublime, so laundry dries at temperatures below 0 ° C.

## Applications

The evaporation energy is mainly used to transport heat.

• Evaporative cooling
• Functional basis of the cooling tower ("trickle cooler")
• "Evaporation refrigerators" that can be operated without electricity
• Wine cooler
• cooling the human body through sweating, for example .
• Refrigeration machine / heat pump : the evaporation heat is absorbed on the side to be cooled (evaporator) and released on the side that is to be heated (condensation).
• When heating by combustion , the combustion reaction product water is produced in gaseous form, the heat of evaporation is bound in the water vapor in the exhaust gas, which condensing boilers can largely recover.

Negative examples are:

• Evaporation cold :
• further cooling of the car windows with wind-favored evaporation of alcohol-containing welding additives; therefore, these mixtures must be designed for much lower temperatures than the outside temperature in winter
• Freezing with wet skin or clothes
• When gas is withdrawn from liquid gas containers, such as carbon dioxide, nitrogen and propane, the pipelines cool down considerably and often have to be heated by convection of the ambient air, for example by means of metal fins.
• Condensation heat:
• Large amounts of energy have to be used to liquefy gases.
• The steam engine and the gas and steam power plant (CCGT) have an efficiency that is reduced by the heat of evaporation of the water, because the waste heat from the condenser (if present) is usually not used.

## Overview of enthalpies of evaporation of the chemical elements

Specific enthalpy of evaporation ΔH v [kJ / g] and the molar enthalpy of evaporation [kJ / mol] of the pure chemical elements for the boiling temperature of the element and a pressure of 1013 hPa. All information was taken from the respective data overviews of the elements mentioned in detail.

Main group elements:

chemical element molar mass [g / mol] Boiling temp. [° C] ΔH v [kJ / mol] ΔH v [kJ / g]
1st main group
Hydrogen (H 2 ) 2.016 −253 0.90 0.446
lithium 6,941 1342 146 21.0
sodium 22.99 883 97.0 4.22
potassium 39.10 759 79.9 2.04
Rubidium 85.47 688 72.2 0.845
Cesium 132.9 705 67.7 0.510
Francium 223.0 677 64 0.29
2nd main group
beryllium 9.012 2477 292 32.4
magnesium 24.33 1090 127 5.24
Calcium 40.08 1484 154 3.83
strontium 87.62 1382 144 1.64
barium 137.3 1640 142 1.03
3rd main group
boron 10.81 3927 490 45.3
aluminum 26.98 2467 293 10.9
gallium 69.72 2204 259 3.71
Indium 114.8 2072 232 2.02
Thallium 204.4 1473 164 0.803
4th main group
Carbon  (subl.) 12.01 4850 717 59.5
silicon 28.09 2355 384 13.7
Germanium 72.64 2820 331 4.56
tin 118.7 2602 296 2.49
5th main group
Nitrogen (N 2 ) 28.02 −196 5.59 0.199
phosphorus 30.97 277 12.1 0.392
Arsenic (subl.) 74.92 616 34.8 0.464
antimony 121.8 1587 77.1 0.634
Bismuth 209.0 1564 105 0.502
6th main group
Oxygen (O 2 ) 32.00 −183 6.82 0.213
sulfur 32.07 445 9.6 0.30
selenium 221 684.6 26.3 0.333
Tellurium 127.6 450 52.6 0.412
polonium 209.0 962 120 0.574
7th main group
Fluorine (F 2 ) 38.00 −188 6.54 0.172
Chlorine (Cl 2 ) 70.90 −34 20.4 0.288
Bromine (Br 2 ) 159.8 +59 29.6 0.193
Iodine (I 2 ) 253.8 +184 41.9 0.164
Astatine 210.0 +337 30th 0.14
8. Main group
helium 4.003 −269 0.084 0.0211
neon 20.18 −246 1.73 0.0859
argon 39.95 −186 6.45 0.161
krypton 83.80 −153 9.03 0.108
xenon 131.3 −108 12.6 0.0962

Subgroup elements: (all data consistent with those given for the individual elements. The specific enthalpy of vaporization was calculated from the molar enthalpy of vaporization; they apply to the boiling point of the elements)

chemical element molar mass [g / mol] Boiling temp. [° C] ΔH v [kJ / mol] ΔH v [kJ / g]
Scandium 44.96 2830 314 6.99
titanium 47.87 3287 421 8.80
chrome 52.00 2672 344 6.62
manganese 54.94 1962 226 4.11
iron 55.85 2750 350 6.26
Cobalt 58.93 2927 377 6.39
nickel 58.69 2913 370 6.31
copper 63.55 2567 300 4.73
zinc 65.41 907 115 1.76
yttrium 88.91 3336 363 4.08
Zirconium 91.22 4409 591 6.47
niobium 92.91 4744 697 7.50
molybdenum 95.94 4639 598 6.23
Technetium 98.91 4877 660 6.67
Ruthenium 101.1 4150 595 5.89
Rhodium 102.9 3695 493 4.79
silver 107.9 2162 251 2.32
Lanthanum 138.9 3457 414 2.98
cerium 140.1 3426 414 2.95
Praseodymium 140.9 3520 297 2.11
Neodymium 144.2 3100 273 1.89
promethium 146.9 3-3500 290 1.97
Samarium 150.4 1803 166 1.11
Europium 152.0 1527 144 0.944
Terbium 158.9 3230 331 2.08
Dysprosium 162.5 2567 230 1.42
holmium 164.9 2695 241 1.46
Erbium 167.3 2510 193 1.15
Thulium 168.9 1947 191 1.13
ytterbium 173.0 1194 127 0.733
lutetium 175.0 3395 356 2.03
hafnium 178.5 4603 575 3.22
Tantalum 180.9 5458 743 4.11
tungsten 183.8 5555 824 4.48
rhenium 186.2 5596 715 3.84
osmium 190.2 5012 628 3.30
iridium 192.2 4428 604 3.14
platinum 195.1 3827 510 2.61
gold 197.0 2856 334 1.70
mercury 200.6 357 59.2 0.295
Actinium 227.0 3200 293 1.29
Thorium 232.0 4788 514 2.22
Protactinium 231.0 4027 470 2.03
uranium 238.0 4134 423 1.78
neptunium 237.0 3902 k. A. -
plutonium 244.1 3327 325 1.33
Americium 243.1 2607 239 0.981
Curium 247.1 3110 k. A. -

Wiktionary: Heat of vaporization  - explanations of meanings, word origins, synonyms, translations

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