Re: Does humidity impact the rate that ice melts separate from heat?

The way you have asked your question provides the key to the answer.  Heat
transfer from warm air circulating around a glass is different from heat
transfer (and mass transfer) by condensation of a liquid on the outside of
a glass.

Generally there are three ways to transfer heat; conduction, convection,
and radiation.

For heat to be transferred by conduction, two solid
surfaces must be in physical contact with each other.  In the case of your
question, heat is transferred through the bottom of your glass by
conduction.  Since metal is a better conductor than wood, cloth, or
plastic, your ice will tend to melt faster when sitting on a metal table
than if it is sitting on a wood or other surface with poorer thermal
conductivity.

Radiation is another way that heat is transferred.  Hot objects (like the
sun) transfer heat by radiation or heat rays.  The hotter the source (and
the cooler the object exposed to the radiation), the more heat is
transferred.  So, keeping a glass out of direct sunlight will also make
your ice last longer.

Convective heat transfer depends upon the movement of fluid (in this case
air) around an object .  As air comes into contact with the cold glass
surface, the air temperature decreases, and the glass temperature
increases.  Ice within the glass will then melt to cool down the glass. 
The rate of heat transfer depends upon the heat capacity of the air, the
amount of surface exposed, the speed of the air, and the temperature
difference between the air and the glass.  If there is wind, more air moves
around the glass, and more heat is transferred (melting more ice).

On a humid day, water vapor in the air will condense on the glass, forming
liquid droplets.  In this case, heat transfer is helped by mass transfer;
you are removing water vapor out of the air and depositing it on your glass
as liquid.  In order to change from gas to liquid, the water vapor in the air
must give up energy; exactly the same amount of energy that it took to vaporize
the water in the first place.  The heat of vaporization of liquid water is
about 540 calories per gram.  When ice melts, energy has to be adsorbed to
change the ice from solid to liquid.  This heat of fusion is about 80
calories per gram.  So, almost 7 times as much heat is required to vaporize
water than to change ice to liquid.  So, if you collect one teaspoon of
moisture on the outside of your glass, you have melted about 7 teaspoons of
ice inside the glass.

Another way to analyze your question is to look at it in reverse.  Let's
say that the next time before you take a shower, you stand in a room, just
to see how fast you cool off.  Then, after taking a shower, you stand in
the same room dripping wet.  As the water evaporates away from your skin, it
will cool you much more rapidly than before you get all wet.

On a humid day, water will evaporate more slowly.  On a dry day, the water
will evaporate more quickly (because there is less water already in the
air). A dry hot day is generally more comfortable than a wet hot day, since
perspiration can dry more quickly in a dry environment. It is also the
reason that dehumidification is an important consideration when purchasing
an air conditioner.

You can find a useful discussion on heat transfer and the latent heat of
evaporation here: http://okfirst.ocs.ou.edu/train/meteorology/HeatTransfer.html

Thanks for an interesting question.