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Specific heat, heat of vaporization, and density of water

Specific heat capacity and heat of vaporization of water. Evaporative cooling. Why ice floats.

Introduction

Let’s imagine that it’s a hot day. You’ve just been out in the sun for awhile, and you’re sweating quite a bit as you sit down and grab a glass of cool ice water. You idly notice both the sweat beads on your arms and the chunks of ice floating at the top of your water glass. Thanks to your hard work studying the properties of water, you recognize both the sweat on your arms and the floating ice cubes in your glass as examples of water's amazing capacity for hydrogen bonding.
How does that work? Water molecules are very good at forming hydrogen bonds, weak associations between the partially positive and partially negative ends of the molecules. Hydrogen bonding explains both the effectiveness of evaporative cooling (why sweating cools you off) and the low density of ice (why ice floats).
Here, we’ll take a closer look at the role of hydrogen bonding in temperature changes, freezing, and vaporization of water.

Water: Solid, liquid, and gas

Water has unique chemical characteristics in all three states—solid, liquid, and gas—thanks to the ability of its molecules to hydrogen bond with one another. Since living things, from human beings to bacteria, have a high water content, understanding the unique chemical features of water in its three states is key to biology.
In liquid water, hydrogen bonds are constantly being formed and broken as the water molecules slide past each other. The breaking of these bonds is caused by the energy of motion (kinetic energy) of the water molecules due to the heat contained in the system.
When the heat is raised (for instance, as water is boiled), the higher kinetic energy of the water molecules causes the hydrogen bonds to break completely and allows water molecules to escape into the air as gas. We observe this gas as water vapor or steam.
On the other hand, when the temperature drops and water freezes, water molecules form a crystal structure maintained by hydrogen bonding (as there is too little heat energy left to break the hydrogen bonds). This structure makes ice less dense than liquid water.

Density of ice and water

Water’s lower density in its solid form is due to the way hydrogen bonds are oriented as it freezes. Specifically, in ice, the water molecules are pushed farther apart than they are in liquid water.
That means water expands when it freezes. You may have seen this for yourself if you've ever put a sealed glass container containing a mostly-watery food (soup, soda, etc.) into the freezer, only to have it crack or explode as the liquid water inside froze and expanded.
With most other liquids, solidification—which occurs when the temperature drops and kinetic (motion) energy of molecules is reduced—allows molecules to pack more tightly than in liquid form, giving the solid a greater density than the liquid. Water is an anomaly (that is, a weird standout) in its lower density as a solid.
(Left) Crystal structure of ice, with water molecules held in a regular 3D structure by hydrogen bonds. (Right) Image of icebergs floating on the surface of the ocean.
Image: modified from OpenStax Biology. Modifications of work by Jane Whitney (left), image created using Visual Molecular Dynamics (VMD) software (Humphrey, 1996), and by Carlos Ponte (right).
Because it is less dense, ice floats on the surface of liquid water, as we see for an iceberg or the ice cubes in a glass of iced tea. In lakes and ponds, a layer of ice forms on top of the liquid water, creating an insulating barrier that protects the animals and plant life in the pond below from freezing.
Why is it harmful for living things to freeze? We can understand this by thinking back to the case of a bottle of soda pop cracking in the freezer. When a cell freezes, its watery contents expand and its membrane (just like the soda bottle) is broken into pieces.

Heat capacity of water

It takes a lot of heat to increase the temperature of liquid water because some of the heat must be used to break hydrogen bonds between the molecules. In other words, water has a high specific heat capacity, which is defined as the amount of heat needed to raise the temperature of one gram of a substance by one degree Celsius. The amount of heat needed to raise the temperature of 1 g water by 1 °C is has its own name, the calorie.
Because of its high heat capacity, water can minimize changes in temperature. For instance, the specific heat capacity of water is about five times greater than that of sand. The land cools faster than the sea once the sun goes down, and the slow-cooling water can release heat to nearby land during the night. Water is also used by warm-blooded animals to distribute heat through their bodies: it acts similarly to a car’s cooling system, moving heat from warm places to cool places, helping the body keep an even temperature.

Heat of vaporization of water

Just as it takes a lot of heat to increase the temperature of liquid water, it also takes an unusual amount of heat to vaporize a given amount of water, because hydrogen bonds must be broken in order for the molecules to fly off as gas. That is, water has a high heat of vaporization, the amount of energy needed to change one gram of a liquid substance to a gas at constant temperature.
Water’s heat of vaporization is around 540 cal/g at 100 °C, water's boiling point. Note that some molecules of water – ones that happen to have high kinetic energy – will escape from the surface of the water even at lower temperatures.
As water molecules evaporate, the surface they evaporate from gets cooler, a process called evaporative cooling. This is because the molecules with the highest kinetic energy are lost to evaporation (see the video on evaporative cooling for more info). In humans and other organisms, the evaporation of sweat, which is about 99% water, cools the body to maintain a steady temperature.

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  • leafers seed style avatar for user miluutin
    In this paragraph of heat of vaporization I got a bit confused by these numbers: "Water’s heat of vaporization depends on the temperature: it's around 540 cal/g at 100 °C (water's boiling point) and around 580 cal/g at 25 °C (room temperature)."
    So in room temperature it needs only (?) 40 calories more to heat up 1C as it takes in the boiling point? How come there is such a tiny difference, or is it actually a huge difference?
    (49 votes)
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    • female robot ada style avatar for user Immanuel Tolstoyevski
      Yes, that part is not very clear. How come only 40 calories can increase the water temperature by 75 degrees to its boiling point, if the specific heat property tells us that 40 calories can only increase it by 40 degrees?

      The relationship is non-linear. Remember that when you apply energy to water, some of it will increase the avg kinetic energy of the molecules (related to the temperature) and some will be spent to break off all hydrogen bonding and send the molecules flying away (related to heat of vaporization at a GIVEN temperature).

      You don't need to wait until 100 degrees for vaporization to begin. It occurs more and more as you near towards it. And as more molecules fly off, less energy is needed to break off the remaining bonds. That's why the difference between heat of vaporization at 25C (energy required to break all H-bonds between 1 gram of initially slow moving molecules) and at 100C (energy to break all H-bonds of 1 gram of fast molecules) is LESS then the energy required to make all of those 1 gram of molecules faster.
      (98 votes)
  • aqualine ultimate style avatar for user JLD
    In the last paragraph it says: "In lakes and ponds, a layer of ice forms on top of the liquid water, creating an insulating barrier..."

    How does ice provide an insulating barrier?
    (24 votes)
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    • orange juice squid orange style avatar for user Ryan Hoyle
      Awesome question. Part of the answer is that less dense materials conduct less heat, and thus slow down heat transfer. If you think about using a metal vs wooden spoon in a hot pan of water, it's the metal one that will burn you, because it is more dense and a better conductor of heat. So the transfer of heat from water to air is slowed down by the layer of ice. Another part of the answer is the ice prevents evaporative cooling, the liquid water molecules become physically trapped and so the ones with the highest kinetic energy can't escape, which would reduce the overall average kinetic energy and thus temperature of the water (see Sal's video on evaporative cooling). Because this doesn't happen with the layer of ice in the way, water can stay warmer for longer.
      (88 votes)
  • orange juice squid orange style avatar for user svetlana4ered
    But why is the distance between molecules in ice bigger than in water? They are still, but why not close enough to each other to make a dense body?
    (21 votes)
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    • duskpin ultimate style avatar for user iShowRizz
      This is because when water goes lower than 4 degrees celsius it expands. Meaning the molecules are further apart. So when water reaches 0 degrees celsius it is frozen at an expanded state. And since it is frozen at an expanded state with molecules further apart, it is less dense than water which has it's molecules closer together.
      (8 votes)
  • piceratops seedling style avatar for user Hikari Akasaki
    Why do the fastest-moving molecules leave the liquid?
    (9 votes)
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  • hopper happy style avatar for user Maryam
    What if you drop a solid into a liquid and they both have the same density. Will the solid float or sink?
    (6 votes)
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  • blobby green style avatar for user Ron  Feldman
    My question is related to the first question listed. The answer seems to contradict what I thought I had learned 50 years ago in high school physics. My question relates to it taking such a small amount of additional energy to raise the temperature 75 degrees when compared to raising it 10 degrees.. I'm afraid I can't articulate my question above or my current understanding below very well.. But here goes..

    What I recall learning is that it took a consistent amount of energy to raise the temperature of a volume of water 1 degree from room temperature up to 99 degrees. But that it took a great deal more energy to raise the temperature that last degree, from 99 to 100, because of the energy required to break the molecular bonds..

    This is my first time using Khan, and I'm excited about having this resource. My thanks to whoever answers this question.. Ron
    (11 votes)
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    • primosaur ultimate style avatar for user Wings of Fire Fan
      In my high school chemistry class(recently), I think what I learned was that the reason a lot of energy is needed during the phase change is because of the energy required to break apart the bonds. I haven't taken physics yet, so I don't know what is being taught now, but it looks like you're pretty much right, at least as far as I know!
      (1 vote)
  • starky sapling style avatar for user Archana
    At the surface of a liquid, why do some molecules evaporate but others do not?
    (6 votes)
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  • scuttlebug blue style avatar for user hannadiop15
    why do some molecules of water escape from the surface of the water at lower temperatures and not others?
    (4 votes)
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    • leaf red style avatar for user Richard
      It’s important to understand what temperature actually is for this question. It is the average kinetic energy of the matter, with the key being average. Not all particles of matter have the same kinetic energy. Some have greater than others, and temperature is simply the mean of those energies. This means that even if some liquid water isn’t at the boiling temperature, there exist some fraction of the water molecules which have sufficient energy to transition to the gas phase. So even though most of the water molecules remain liquid, the most energetic water molecules escape the liquid as water vapor.

      Hope that helps.
      (9 votes)
  • duskpin ultimate style avatar for user Marwan
    what is the difference between heat and temperature?
    (5 votes)
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  • blobby green style avatar for user Quin Keza
    i don't understand really well how hydrogen bonds are oriented in ice
    (5 votes)
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