## Sunday, January 8, 2012

### Why Water Feels Colder Than Air

Air at 80°F can feel uncomforably warm.  Water at 80°F can cause hypothermia.  Why is it that if one has water and air both at 80°F that the air will feel warm and the water will feel cold?  It turns out there are several reasons why water feels colder than air.  If you've never thought about this before I suggest you stop to ponder it for a few moments before continuing on.

Heat vs Temperature
I'll begin with one of my trademark unnecessary background explanations.  Heat is a form of energy.  It manifests itself as kinetic motion in molecules bouncing around off each other.  Temperature on the other hand can be thought of as the average heat energy an object has (with some exceptions).  This is very similar to the relationship of mass and density.  If one wishes to increase density one can either increase the mass (while keeping volume constant) or decrease volume (while keeping mass constant).  Similarly, to increase temperature one can either increase heat energy, or decrease the volume (while keeping the other constant).  The classic example of this a bike pump feeling warm because of compressed air, or some sort of compressed air feeling cold when it's allowed to decompress.

An example I saw Bill Nye do once is the comparison of a lit match to an ice sculpture.  Clearly the burning match has a much higher temperature.  However, since there is simply so much more ice, the sculpture has more heat energy.  To revisit our mass and density analogy, styrofoam has a much lower density than lead.  However, a large block of styrofoam would have a much higher mass than a small pellet of lead.

Another issue that should be addressed is why things feel cold in general.  Your body is warm, and most things in the environment are colder than it.  When your warm body comes in contact with something colder than it, heat from your body moves to the object.  This leaves your body with less heat, and thus less temperature.  The transfer will continue until you body and the object are equal in temperature.  Since your body will continuously adjust its temperature back to normal, in practice this means your body will give heat energy to the object until it reaches body temperature.

Now that we understand the difference between heat and temperature, we can begin addressing the specific reasons why water feels colder than air.  There are five effects that could explain this.  Different combinations of effects will apply depending on the situation.

Denser
At the temperatures we are talking about water is liquid and air is a gas.  This means water is much denser than air.  Since density is simply the measure of mass in a certain volume, the higher density means more mass of water in the same volume of air.  Mass is often the best way to talk about how much of something there is.  In this case, since liquid water is denser than air, it simply means there is more water in the close space around your body.  This means it will take more heat energy from your body to warm the water up to body temperature than if it were the less dense air.

At room temperature a cubic meter of water has a mass of 998 kg, while the same volume of air has a mass of 1.225 kg.  The same volume of water as air has about 815 times the mass.

Specific Heat
We know that more mass will take more energy to warm up.  You may be asking yourself if that is the only thing that matters.  Will two different substances, of equal mass, require the same energy to cause the same rise in temperature?  The answer is no.  Every substance has an intrinsic property called "specific heat" that determines how much energy is required to raise the temperature of an equal mass by an equal amount.  The formula for temperature change is: $T = \frac{Q}{c m}$ Where: T is change in temperature, Q is heat energy, c is specific heat, and m is mass.  This can be viewed as saying, a given amount of heat energy will result in less of a temperature increase the higher the product of mass and specific heat is.

Water has many interesting and unique properties.  One of these is a very high specific heat.  The only known substance with a higher specific heat is ammonia.  This is largely the result of strong attractive forces between molecules, known as hydrogen bonding.  At room temperature the specific heat of water is 4.1813 $\rm{\frac{J}{g K}}$, and air is 1.012 $\rm{\frac{J}{g K}}$.  This about 4.13 higher.  Since we saw that specific heat is multiplied by mass, and the mass is also much higher for the same volume, we can look at the combined specific heat times mass of water vs air.  This combined product is about 3366 times higher for water than for air.

Forced Convection
When a fluid like water or air is in contact with your body it is warmed and then becomes less dense, and thus floats on top the rest of itself.  New unwarmed fluid moves in to next to your body and that must then be warmed.  This process is called convection.  In practice convection isn't that significant.  However, forced convection is.  Forced convection simply means that the air or water near your body is being forced to move away instead of naturally floating away.  This is how a fan or wind cools your body.

If you are in a pool of water vs standing in air there isn't much difference in terms of convection.  However, if the water is flowing over you then that is a very significant factor.  In the case of rain or a shower, water is in contact with your body for a few seconds and then leaves, taking whatever heat your body invested in it with it.  In a pool of static water or air your body could bring the temperature up to its own, and then the heat transfer would stop (ignoring gradual convection).  But if water is rushing by this can never happen.

Thermal Conductivity
When two objects of unequal temperature are in contact heat flows from the higher temperature object to the lower temperature one.  This is conduction, one the the three types of heat transfer.  How quickly heat is transferred will depend on the thermal conductivity of the substances.  Water and air have different thermal conductivities.  While, water's isn't that special, air's is very low.  This means air absorbs heat much slower than water does.  Liquid water has a thermal conductivity of about 0.6 $\rm{\frac{W}{m K}}$, compared to air at 0.025 $\rm{\frac{W}{m K}}$.  Heat energy is transferred about 24 times faster through liquid water than through air.

Latent Heat of Vaporization
I said above that if volume is held constant, an increase in heat will cause an increase in temperature.  This is true except for when the substance is undergoing a phase change.  In other words, while it is melting or vaporizing, there is heat being added, but the temperature does not go up.  Here is a graph that shows this.  Note the amount of heat energy (x axis) needed to raise water from freezing to boiling vs the amount needed to actually vaporize it.  To vaporize (boil or evaporate) a kg of water takes 2257 kJ of energy.  This is over five times the energy needed to raise water from just above freezing to just below boiling.  To make this clear, it means that causing a kg of water to evaporate requires many times more energy than warming ice water to body temperature.  That energy comes from your body heat, and this is exactly how sweat cools your body.

Like forced convection, evaporation may not occur in all situations.  If you are submerged in water there will be no evaporation.  And, if there is 100% humidity then the air is already saturated with water and there can be no more evaporation. This is likely the case in a shower or in rain.  However, afterwards the humidity can drop.  There is a good chance that the water on your body will have already warmed to body temperature, which will remove all the other effects.  At that point, evaporation alone is what would cause the heat loss.

To summarize:
Water feels colder than air because there is more water near your body (denser), which takes more heat to bring to body temperature (specific heat), and takes heat from your body faster (thermal conductivity).  This water may then be flowing away from your body, taking the heat with it (forced convection), or evaporating and consuming a huge amount of energy to do so (latent heat of vaporization).