Friday, February 24, 2012

Latent heat of vaporization and of fusion explained by the kinetic theory

Cooling by evaporation experiment
Latent heat graph

Latent heat of vaporization

  Most of my students did not completely understand latent heat. So I will try to keep it as simple as possible.
  When a kettle is put on a boil the temperature of the water steadily rises until it reaches 100 °C. At this temperature it starts to boil, that is to say bubbles of vapour form at the bottom and rise to the surface, where they burst and escape as steam.
  Once the water has begun to boil, the temperature remains constant at 100 °C. But at the same time, heat is being steadily absorbed by the water from the gas flame or heating element.
This heat, which is going into the water but not increasing its temperature, is the energy needed to convert the water from the liquid state to the vapour state.
  Experiment shows that 2260000 J are required to convert 1 kg of water at its boiling-point to steam at the same temperature. This is known as the specific latent heat of steam. The word "latent" means hidden or concealed. This extra heat goes into the vapour but does not indicate its presence by producing a rise in temperature.
  When the steam condenses to form water the latent heat is given out. This is one reason why a scald from steam does more harm than one from boiling water. Other liquids besides water absorb latent heat when they turn into vapour. For example, 860000 J are required to convert 1 kg of alcohol at its boiling-point to vapour at the same temperature. These quantities of heat are called the specific latent heats of vaporization.

Definition of the specific latent heat of vaporization

  The specific latent heat of vaporization of a substance is the quantity of heat required to change unit mass of the substance from the liquid to the vapour state without change of temperature. ( Symbol = L ).

  The SI unit of specific latent heat of vaporization is the Joule per kilogram ( J / kg ). However, in order to avoid having to write every large numbers the alternative units kj / kg or MJ / kg may be used instead.
    1 kj = 1000 j

    1 Mj = 100000 j

  So we may express the specific latent heat of vaporization of water as 2260 kj / kg or 2.26 Mj / kg. ( The old thermal unit was calorie per gram ( cal / g ) ).

Latent heat of fusion

  Just as latent heat is taken in when water changes to vapour at the same temperature, so the same thing occurs when ice melts to form water. But in this case the latent heat is not so great. It requires only 336000 j to convert 1 kg of ice at 0 °C to water at the same temperature. Likewise, when water at 0 °C freezes into ice, the same quantity of heat is given out for every 1 kg of ice formed. This is called the specific latent heat of ice.
  As already mentioned, the phenomenon of latent heat is not confined to water alone. Other substances also absorb latent heat when they melt; conversely, they give out latent heat on solidifying. This heat is called latent heat of fusion.

The specific latent heat of fusion

  The specific latent heat of fusion of a substance is the quantity of heat required to convert unit mass of the substance from the solid to the liquid state without change in temperature. ( Symbol = L. ).

  The SI units, j / kg, or alternatively kj / kg or Mj / kg, are used for fusion as for vaporization.

To measure melting point from a cooling curve

  The latent heat given out when a molten substance freezes to the solid state may be shown by the following experiment with naphthalene. Naphthalene is a white crystalline solid obtained from coal-tar. It has a pungent smell and is often used by gardners as a soil fumigant.

The experiment

  1- A test-tube containing naphthalene is held vertically by a clamp and stand.

  2- The naphthalene is heated gently by a very small bunsen flame until it just melts.

  3- A thermometer is inserted in the naphthalene and the heating continued until the temperature of the melted naphthalene is about 100 °C.

  4- The bunsen flame is then removed, and readings of the thermometer are taken at minute intervals as the tube and its contents are cooling

  What we will notice?

  It is noticed that when the freezing point, or what is the same thing, the melting point, of the naphthalene is reached the temperature remains constant at 80 °C untill all the naphthalene has solidified. After this temperature begins to fall again.
  Cooling curve for naphthalene
The temperature changes are illustrated most strikingly by plotting a graph of temperature against time. The flat portion of the graph represents the time during which the naphthalene is solidifying. At this stage its temperature remains constant at 80 °C although heat is steadily being lost by convection and radiation all the time.

The heat lost is exactly compensated by the latent heat of fusion of the naphthalene, which is being given out during the change from the liquid to the solid state.

  Other substances, for example paradichlor benzene, can be used in this experiment and their melting points found from the flat portion of the cooling curve.

Cooling produced by evaporation- Volatile liquids

  Some liquids have a low boiling-point, and thus change from liquid to vabor quite easily at ordinary temperatures. These are called volatile liquids. Methylated spirit and ether are examples.
  If a little methylated spirit or eau-de-Cologne is split on the hand it evaporates rapidly and the hand feels very cold. To change from liquid to vapour, the spirit requires latent heat. This it obtained from the hand, which thus loses heat and cools. Water would also cause the hand to become cold, but not so noticeably as methylated spirit. The spirit has a lower boiling-point than water, and so it evaporates more quickly at the temperature of the hand.
  Campers are well aware that milk can be cooled more efficiently by wrapping the bottle in a wet cloth than by standing it in a bucket of cold water. If the rate of evaporation can be speeded up by placing the wet bottle in a draught, so much the better.
  Perspiration is the body's method of maintaining a constant temperature. When perspiring heavily after exercise it is unwise to stand about in a draught, or overcooling may result from evaporation. The resulting chill may lower the resistance of the body to infection.
  Dogs, who do not perspire from the skin, hang out their tongues during hot weather in order to achieve a cooling effect.

To make ice by the evaporation of ether

  1-A beaker about one-third full of ether is stood in a small pool of water on a flat piece of wood.
  2- A current of air is then bubbled through the ether by means of a rubber tube attached to bellows.

  3- The ether evaporates into the bubbles, and the vapour is carried quickly away as the bubbles rise to the surface and burst, thus increasing the rate of evaporation.

The rapid change from the liquid to the vapour state requires latent heat. This comes from the liquid ether itself, with the result that it soon cools well bellow 0 °C.

At the same time heat becomes conducted through the walls of the beaker from the pool of water below it, and eventually the water cools to 0 °C. After this it begins to lose latent heat, and freezes.

Cooling by evaporation explained by the kinetic theory

  The molecules of a liquid have an average kinetic energy which increases with temperature.
  Molecules near the surface which happen to be moving faster than average can escape from the attraction of their neighbours and jump out of the liquid. Some of these may collide with other molecules above the liquid and so bounce back into it. But many others may escape altogether and their escape will be assisted if a current of air is passed over or through the liquid. Bubbling air through a liquid also increases the rate of evaporation by increasing the surface area from which molecules may escape.
  In this way the liquid loses its most energetic molecules while the less energetic ones are left behind. The average kinetic energy of the remaining molecules is therefore reduced and this results in a fall in temperature.

Fusion and vaporization in relation to the kinetic theory of matter

  We explained on :About atoms and molecules that the molecules of solids vibrate to and fro alternately attracting and repelling one another. Their total energy can be looked on as consisting of two parts:

  1- Kinetic energy which depends on the temperature; and

  2- Potential energy which depends on the force between the molecules and their distance apart.
  In the liquid state the molecules have a wider range of movement than in the solid, thus going into extra close and extra distant positions.Their potential energy is therefore increased and the additional energy required is the latent heat of fusion.

  Vaporization when heat is supplied

  When vaporization occurs the vapour occupies a much larger volume than the liquid so that energy is required to seperate the molecules against their mutual attractions ( internal work ). In addition extra energy is required to enable the vapour to expand against the atmospheric pressure ( external work). The heat required to provide the sum total of internal and external work without change of temperature is the latent heat of vaporization.