From what height should a drop of water fall in order for it to boil when hitting the ground?

From what height should a drop of water fall in order for it to boil when hitting the ground? Consider that the droplet is heated by 50% of the consumed mechanical energy. The initial water temperature is 20 degrees.

Given:

t1 = 20 ° Celsius – initial water temperature;

t2 = 100 ° Celsius – the temperature at which water boils;

n = 50% = 0.5 is the amount of energy spent on heating the drop;

g = 9.8 Newton / kilogram – acceleration of gravity;

c = 4200 Joule / (kg * C) – specific heat of water.

It is required to determine h (meter) – from what height the drop must fall to boil.

Let the droplet mass be equal to m. Then, according to the law of conservation of energy, the potential energy of a drop located at a height h should be sufficient for boiling, that is:

n * E (potential) = Q;

n * m * g * h = c * m * (t2 – t1);

n * g * h = c * (t2 – t1);

h = c * (t2 – t1) / (n * g) = 4200 * (100 – 20) / (0.5 * 9.8) =

= 336,000 / 4.9 = 68,571 meters (the result has been rounded up to whole integers).

Answer: to boil, a drop must fall from a height of 68571 meters.