... or how water saves the day.

In early spring, weather can be very capricious and every farmer fears temperature changes. When the weather gets warm enough, the vine buds and benefits from the sun. But all of a sudden the thermometer decreases below 0°C (32°F) during the night and the irreversible happens : the newly-born buds are killed by the frost. Damn'it ! The grape harvest will be bad this year...

Hopefully there is an ancient technique to prevent that. And what makes it almost magic is that only water is needed to save the crops. The idea is to keep an eye on the thermometer and when it's heading for 0°C, start spraying the vine (ar any other fruit tree) with water. A miracle is about to happen : if the weather does not become too cold, the poor defenseless buds will be saved.

There is no miracle

Now I swap my farmer's hat with that of a physicist and this castratrice action replaces all magic with plain factuals. No it is not a miracle if the buds were saved by water, it has to do with thermodynamics.

Thermal exchanges are energy exchanges and energy is expressed in Joule. When you heat an object, you give it a certain amount of energy. The temperature change reflects the amount of energy given. From the definition of enthalpy :

ΔH = cp ΔT, (cp > 0 in J/kg/K, T in K or C)

When the air is cooler than the object, it is in fact the object that heats the atmosphere. It gives away energy (ΔH < 0) hence its temperature decreases (ΔT < 0) and the buds frost.

This is the case when there is no phase change. During a phase change, the temperature (of a pure substance) is constant (the phase change temperature) although energy is still exchanged. The heat absorbed by a substance as it changes phase from liquid to solid is called the Latent Heat of Fusion Lf and it is expressed in J/kg. The Latent Heat of Fusion of water is Lf = 334 kJ/kg which means that you must give 334 kJ to a 1 kg ice cube at 0°C to melt it completely (expose it for 5 min to a 1000 W radiator). By the end of an operation you will have 1 kg of water at 0°C.

1 kg of water releases 334 kJ when it changes from liquid to solid phase. The cold freezes the water which stays at 0°C during this process and protecs the buds. This is why farmers spray their vines with water when the weather gets cold.

What is it worth ?

Now let's get an idea of how efficient this technique is. Newton's conducto-convective law established a relation between the difference of temperatures between two substances and the amount of energy exchanged :

Φ = h (Tair - Twater) is the thermal flux (W/m2) released by the water into the atmosphere.

h is Newton's conducto-convective coefficient which ranges typically from 5 to 1000 W/K/m2.

|  XXX  |
|  XXX  |  vine branch surrounded with water
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Let V be the volume of water, m the mass of water and S the surface in contact with the atmosphere. The energy released by the water when it changes phase is Q = m · Lf. The power exchanged is P = S · h · (Tair - Twater). Hence the water will frost in t = - Q / P seconds :

t = - m · Lf / ( S · h · (Tair - Twater) )
Here is the model :
Length of vine branch : 1 m
Diameter of vine branch : 0.01 cm
Mass of water : m = 100 g
Latent Heat of Fusion of water Lf = 334 kJ/kg
Exchange surface : S = 0.03 m2
Newton's conducto-convective coefficient air/water : h = 50 W/K/m
Tair = -5 °C
Twater = 0 °C
t = 4446 s = 1h 14 min

Closing words

This method does indeed save the buds from frost but the temperature must not be too low for it to function correctly. The same idea was used to prevent cellars from freezing during cold winters. People just filled them with buckets of water because they release energy when they change phase.

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