Freezing Food Without a Freezer: The Salt–Ice Mixture Bound — Lowest Temperature, and the Ice and Salt Consumed per Kilogram Frozen

Mixing salt into crushed ice produces a brine that stays liquid well below 0 °C, and food buried in the mixture can be frozen without any machinery — a method that predates mechanical refrigeration and is still used for hand-made ice cream and emergency cooling. This paper computes the thermodynamic bound on the method: the lowest temperature each common salt can reach, and the ice and salt consumed per kilogram of food frozen from 30 °C to a stated storage temperature. The lowest attainable temperatures are set by the eutectics of the salt–water systems: −21.1 °C for sodium chloride and about −51 °C for calcium chloride. Freezing 1 kg of a high-moisture food from 30 °C to −18 °C requires removing 392.7 kJ and consumes 1.52 kg of ice and 0.40 kg of sodium chloride (1.92 kg of mixture in total), or 1.52 kg of ice and 0.36 kg of calcium chloride. Sodium chloride reaches the standard −18 °C storage temperature with only 3.1 K of margin above its eutectic, so in practice it operates at the edge of its capability and any heat leak into the container pushes the food above the target. Colder targets cost steeply: calcium chloride at −30 °C consumes 1.99 kg of ice and 0.70 kg of salt per kilogram of food, and at −40 °C it consumes 2.61 kg of ice and 1.07 kg of salt, a total of 3.67 kg of mixture per kilogram of food, which crosses the paper's stated practicality limit of 3 kg of mixture per kilogram of food. In a hand-worked tub holding 15 kg of mixture, the largest single batch is 7.8 kg of food at −18 °C with sodium chloride, falling to 4.1 kg at −40 °C with calcium chloride. A 25 kg load at −18 °C with sodium chloride needs 38.0 kg of ice and 10.0 kg of salt. The method is sound for small, occasional loads near −18 °C and stops being practical for large loads or for temperatures far below the sodium chloride eutectic.