How this calculator works
A drink cools because heat flows from the liquid to the colder surroundings. When the container is small and the surroundings move heat well, the whole drink stays close to one temperature and Newton's law of cooling applies: the rate of cooling is proportional to the difference between the drink and its surroundings. The result is an exponential approach, described by a time constant. A thin aluminium can in an ice bath cools in minutes, while the same can in a still fridge takes about an hour. The model assumes a well-mixed drink and a constant surroundings temperature.
Formula
temperature at time t = surroundings + (starting temperature - surroundings) x exp(-t / tau). time to reach a target = tau x ln((starting - surroundings) / (target - surroundings)). tau = mass x specific heat / (heat transfer coefficient x surface area). The calculator uses 4186 J/(kg K) for water and 8 to 12 W/(m2 K) for air, and 500 W/(m2 K) for a water or ice bath.
Worked example
A 330 mL can of beer at 22 °C in a fridge at 4 °C, with a heat transfer coefficient of 10 W/(m2 K). The can has a surface area of about 0.0321 m² and holds 0.33 kg, so tau = 0.33 x 4100 / (10 x 0.0321) = 4,210 s, or 70 minutes. To reach 6 °C, the time is 4,210 x ln(18 / 2) = 9,250 s, or 154 minutes. In an ice bath at 0 °C the time constant falls to about 84 s, and the same cooling takes 185 s, about 3 minutes.
Advertisement
Frequently asked questions
Why is an ice bath so much faster than the fridge?
Water carries heat away from the can far better than air, and melting ice keeps the bath at a steady 0 °C. The heat transfer coefficient in water is roughly fifty times that in still air, which is why a drink can chill in minutes rather than hours.
Does a can cool faster than a bottle of the same volume?
Usually, because a can has a larger surface area relative to its volume and a thin metal wall with little insulation. A glass bottle has thicker walls and often a smaller area for its volume. The calculator accounts for both the container size and the drink inside.
Should I put warm drinks in the freezer?
It is faster, but a drink left too long can freeze, expand and break a glass bottle or burst a can. Set a timer and use the freezer setting as a short-cut only. Never put a sealed carbonated container in a freezer and forget it.
Why does the model not predict the last degree?
As the drink approaches the surroundings, the temperature difference shrinks and cooling slows down. The exponential never quite reaches the surroundings temperature, so the time to the last fraction of a degree is very long. Choose a realistic target, such as 6 °C for a refreshing drink.