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"As the drink cools more water melts into the drink, diluting the cocktail. Thus a shaken Martini is generally slightly stronger than a stirred one."

When a drink is shaken, or stirred, with ice, the cooling happens as the heat from the drink is used for melting the ice, tying together the cooling and the diluting.

If the drink was mixed in a completely insulated container (= adiabatically), both shaking and stirring would result in exactly the same amount of ice melting, for exactly the same amount of cooling of the drink. Shaking just makes the heat exchange happen faster, by moving the liquid more over the ice surfaces.

In practice I would guess, (1) we rarely have the patience to stir a drink long enough to cool it as cold as a vigorous shake accomplishes, so I'd guess that actually the shaken drinks are colder, thus a little more diluted by water.

Or, if we really stir and shake until the same temperature, stirring takes longer, so there is more time for non-adiabatic effects: (2) more time for heat exchange with air, so maybe stirred are more diluted.

Then again, (3) usually we stir in a glass container but shake in a metal container, and metal has higher thermal conductivity, so actually cooling both the drink and the container walls would use more heat (=more melted ice) when shaking.

I'd guess that effects (1) and (3) are stronger than (2), and thus shaken drinks would be more diluted that stirred.



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