There are three processes to take into account:
- The warming of ice towards the melting point if it was originally below $0^{\circ} C$.
- The melting of ice itself
- The warming of the resulting water
The 1. and 3. part is addressed by heat capacity of ice and water respectively and the amount of heat will be directly proportional to temperature difference and weight of the water/ice. The proportionality constant (actually it also depends on the temperature but not very strongly so let's just ignore that) is called specific heat. For water it is about twice as large as that of ice at temperatures around $0^{\circ} C$.
As for the 2. part, this has to do with latent heat. Simply put, this is an amount of heat you need to change phases without changing temperature. Less simply put, when warming you are just converting the heat into greater wiggling of water molecules around their stable positions in the crystal thereby increasing their temperature. But at the melting point that heat will instead go into breaking chemical bonds between molecules in the ice lattice.
Now, latent heat is really big (you need lots of energy to break those bonds). To get a hang on it: you would need the same amount of heat to warm water from $0^{\circ} C$ to $80^{\circ} C$ as you would need to melt the same amount of ice.
Now, presumably you want your drink cold in the end so that temperature for 3. will be close to $0^{\circ} C$ and also the ice cubes should be pretty warm (no use in producing ice cubes of e.g. $-50^{\circ} C$, right?). This means that these processes won't contribute much cooling. It's fair to say that melting of the ice takes care of everything.
Note: we can also quickly estimate how much ice you need by neglecting the processes 1. and 3. Say you are starting with a warm drink of $25^{\circ} C$ and you want to get it to $5^{\circ} C$. So, reusing the argument about the $80^{\circ} C$ difference being equivalent to a latent heat of the same mass, we see that you need four times less ice than water to get the job done.
Privět. These are real-world questions that NASA, Russian/Soviet space program, and others of course had to be solving – if you kindly believe that astronauts are real – when they were designing space suits, see e.g.
http://en.wikipedia.org/wiki/Spacesuit
Actually these 8 pages about space suits could be more useful (buttons 1-8 are at the bottom):
http://science.howstuffworks.com/space-suit1.htm
Space suits only give the astronauts oxygen – from the spaceship – and have to remove carbon dioxide that the astronaut breathes out. Neoprene and other layers of fabric isolate the astronaut at the inner side. The outer side is "white" – it is made out of a highly reflective material so it doesn't really absorb much of the intense solar radiation that you were sensible worried about.
There's extra heat from sweating. Gemini and Mercury programs used cool air. Since the Apollo program, NASA has been using water cooling. All the required material has to be available in the space suit and/or the spaceship. You essentially propose to equip space suits with an active fridge. In principle, it's a good idea but it's hard to quickly get rid of the heat without a "reservoir", anyway.
A human consumes 2,000 kcal a day – the heat needed to warm 2,000 kg of water by 1 °C (or 200 liters of water by 10 °C, and so on). That's the usual "recommended nutrition value". In normal units, that's about 8,000 kJ a day. Most of this energy ultimately ends up as heat. When divided to 86,400 seconds, you get about 90 W. Well, at rest, a human actually produces about 70 W (70 Joules per second) of heat. It's like a classical light bulb.
However, you don't have to remove all this heat manually. Much of it is just radiated away by thermal radiation.
Of course, spaceships have to deal with much greater amounts of energy to move, cool the engines that heat up, and so on. Fuel for a space shuttle includes a ton of liquid hydrogen plus tens of tons of liquid oxygen – that's energy comparable to 140 GJ or so when burned. If it were used to replace the heat from an astronaut, it's enough for billions of seconds.
Space shuttles were cooling inner surfaces of nozzles by liquid hydrogen. Note that the latent heat of hydrogen is 461 kJ/kg. I said that a human produces 8,000 kJ of heat a day – it is just the vaporization of 20 kg of hydrogen (per day) if you needed to manually remove all the heat which you don't have to.
The International Space Station where astronauts spend years needs a long-term solution, a cooling system that was developed by Boeing and contains many components. In some of them, ammonia is used.
There are lots of engineering issues but the things work when the dust is settled and bugs are fixed. You should understand that while the astronauts need oxygen and other things, they're not really "depending on every second of life support" when it comes to the temperature. When you're isolated enough, you may survive at the North Pole or the equator. The outer space (with a space suit) isn't too different in this respect.
See also a question on oxygen production at the ISS etc.:
How do they produce air on the ISS?
Best Answer
and:
The latter statement you quoted is frankly speaking pseudo-scientific poppycock.
Maintaining high rates of cooling water always promotes cooling: heat energy carried off per unit of time is increased.
High cooling water flow rates increase heat transfer coefficients (by promoting turbulence), as well as keeping the cooling water at lower temperature, which further promotes cooling, as the heat carried off per unit of time is directly proportional to the temperature difference between the cooling water and the object to be cooled (see Newton's law of cooling).
Of course there may be other, practical limitations to cooling water rates, such as pump rating and pressure build up. But within these margins, the faster the flow of cooling water, the better the cooling.