Probably better to seal the ice in something so that the melt cannot enter the beverage.
Of course the other factor not mentioned here is that to many discerning tastes (this is code for “my taste” ;)) the gradual diluting effects of melting ice are actually desirable. In fact, the secret to making certain types of mixed drink great is using lots of good fresh ice.
Francis - did you inadvertently mess up the calculation ?
Using your numbers (and assuming there is no freezing - no latent heat calcs), the equation for the final temperature I get is :
0.1x10^3x(T-77) = 0.15x3.5x10^3x(300-T)
Solving for T, gives me T = 264.3 K or 16 deg F or -8.8 deg C - this will be a great drink to have.
That would be hard to get from gin in a freezer :).
(Freezing point of alcohol+water mixture with 40% v/v alcohol is about -23C (-10F) - so we are lucky the above calc works. )
Also - nitpick (in the spirit of the SDMB): In general, Specific heats scale with weight percentages for liquid (not volume percentages).
That would be hard to get from gin in a freezer 
I agree for certain stuff fer sure. I like to drink barrel-proof bourbon with a big ice cube and taste the gradual shift in flavors as the spirit is diluted. FWIW, I will also drink a rocks martini sometimes too.
Quite probably. I did them sitting in bed as I wrote the reply. I should physically write it down as I go, but it was late and I was too tired.
Agree. However the specific gravity of alcohol is 0.9, and the ratios sufficiently flexible that I didn’t bother to do the conversion. However I should have said so.
Indeed.
Glad someone checked. I wrote the reply more to indicate the thought process required, and less to get the precise answer.
And to follow up - mistake is trivially stupid. As a rough approximation the energy that the glass will suck out is not 1/20, it is (300 - 77) * 1/20 = 1/5 which is a big enough change that a proper solving of the equation is needed.
So, the answer would appear to be that if you cool at least the main part of the glass with LN[sub]2[/sub] you can get an instant well cooled Martini. So long as the glass doesn’t break. The above comments on stopping things heating up before you add the ingredients apply. Whether swilling some LN[sub]2[/sub] around in the glass for a moment will do the job is hard to judge. We start to get into latent heat calculations, and we don’t really know how carefully the cooling is done.
If you pour a couple jiggers of liquid nitrogen into the glass and then pour your cold Sapphire in on top of that, I imagine it would be kind of like dumping red lava into water. By the time you get to taking the first sip, all the nitrogen would have boiled harmlessly away, right?
Sure, but the drink that you want cold would also be blown away, as the rate of N2 boiling increases, pressure increases…
Best to cool the glass , ensure there is no “boiling” going to happen in the glass, and then put the drink in…
I’m guessing what they do is to stir their Manhattans/Martinis with lots of ice, strain it out (only so much ice will melt and the drink will only get so cold), and then plopping the big ice cube in as much as decoration as to keep the drink cold.
How about something that freezes at 0 C (or, with some alcohol or something added, down to negative teens C), and besides the heat of fusion, has a heat capacity as high as or higher than a mixed drink?
Hmm… you think that could work? Not really a solution for bars, but for home use, there might be something to that idea…
For round numbers the “heat capacity” of a mixed drink is that of water. Which has an almost magically high specific heat.
IMO if that substance existed, we’d have been using it to cool drinks for the last 100 years.
You could make several chilled martinis and pour them into an insulated thermos. Refill into a standard martini glass, or depending on how discrete/bourgeois you wish to be, drink directly from the thermos.
Or how about a double wall insulated martini glass? You’d effectively be removing 2/3 of the heat transfer surface area.
A local restaurant used to serve it’s martinis in aluminum ‘glasses’. It kept the drink cool longer than glass. I have a double walled aluminum coffee mug that keeps my coffee comfortably warm for more than an hour, granted it does have a lid. Perhaps the double-wall thing would work for cocktail glasses?
We certainly would have. At least 150 years, I’d think.
(I… honestly can’t tell if you missed my point or are playing along… In case you’re not, you should see what’s inside the objects I linked to, which is a substance with an almost magically high specific heat, far more than the objects enalzi linked to.)
Huh, never knew that. Would have thought there’s still enough water in there for it to freeze. Is that true for any 40% alcohol liquor? What about a 35 or 30%? I think I might try some home experiments now. 
That’s just for ethanol/water mixtures. I expect sugar to depress the freezing point further.
Thanks for the chart. Now if I only knew what temperature my freezer was set to! (All I have is a lousy dial which literally reads “Normal - Cold - Colder”. I guess numerical temperature would just be too darn fancy and impossible for the layperson to understand)
Clearly you need to make multiple samples and see which ones freeze. Dispose of all samples properly 
Referring to The Thin Man, one sees the proper size of a martini glass.
Modern martinis are often made extra large. Which leaves you with a glass half full of lukewarm gin. Or–even worse–vodka.