Boiling water and frost

BOILING WATER

The dependence of the freezing time of 1 ka of water on the initial temperature is shown on the figure red line. On the left - when water evaporates into a vacuum; on the right - at an external pressure equal to the saturated vapor pressure above the surface of supercooled water with a temperature of minus 10 ° C.
The dotted green curve shows the relationship

There are two glasses in front of you. One with boiling water, and the second with tap water. In which of them will the water freeze first if the glasses are exposed to frost?

The answer seems obvious: of course, boiling water will take longer to freeze. After all, by the time the hot water cools down to the cold temperature, it will already begin to freeze.

However, if you place two wooden tubs with cold and hot water outside in winter, the hot water will freeze faster than the cold. Let’s close the tubs with lids - the effectiveness will disappear. Let’s pour water into metal barrels - again nothing unusual will happen.

The phenomenon, which seems paradoxical at first glance, has a simple physical explanation.

Water will freeze at 0° C. First it cools to this temperature, and then ice begins to form. This applies equally to both cold and hot water. How is the water already cooled?

When answering this question, two processes should be taken into account: heat exchange with the environment and evaporation. If the vessels are made of a good insulator, for example, wood, then heat transfer through the walls is difficult and cooling occurs mainly due to evaporation from the surface.

During evaporation, a region of vapor is formed above the surface of the liquid, the pressure of which changes all the time. If the vessel is closed, then this vapor quickly becomes saturated with a pressure $P_H$ equal to the saturated vapor pressure at a given temperature.

Then further cooling occurs almost entirely due to heat exchange.

Completely different phenomena occur in an open vessel. As already said,

The maximum time it takes for water to cool from the initial temperature to 0°C, and the dotted yellow curve shows how long it takes for the remaining water to freeze after cooling to 0°C. A unit of time is taken to be the time during which water freezes, having an initial temperature of 0°C and placed in a vacuum.

AND FROST

the liquid evaporates until equilibrium with steam is established, that is, until the pressure above the surface of the liquid becomes equal to $P_H$. The saturated vapor pressure $P_H$ depends on temperature and increases with increasing temperature. Therefore, the vapor pressure over the hot liquid is less than $P_H$, and due to intense evaporation it quickly cools. During evaporation, the mass of water naturally decreases all the time, and therefore, when the temperature becomes equal to 0°C, there will be less hot water left in the “hot” vessel than in the “cold” one. Further cooling of the liquid in both vessels will occur under the same conditions. And since there is less water left in the “hot” vessel, it will freeze even faster. The phenomenon described was studied by the Canadian physicist Kell. He took two thermoses with a wide neck and filled each with 1550 grams of water, and in one thermos the water temperature was $t_1=88°С$, and in the second $t_2=56°С$.

The thermoses were placed outside at an air temperature of minus 6.5°C. When $t_1$ became equal to 39°C, only 1430 grams of water remained in the “hot” thermos, and in the end it froze even more than the water in the “cold” thermos.

It turned out that during cooling from 100°C to 0°C, water loses 16% of its mass, and when freezing - another 12%, that is, the ice obtained is 28% less than the original amount of water. It was also found that from the boiling point to 50°, water cools about 9 times faster than from 50° to 0°. Thus, under certain conditions, when heat exchange with the environment is difficult and the free surface of the liquid is exposed to liquid, boiling water will freeze faster than tap water.