Estimate how high a drop of water should fall so that it boils when it hits the ground. The initial droplet temperature is 20 ° C

Estimate how high a drop of water should fall so that it boils when it hits the ground. The initial droplet temperature is 20 ° C; air resistance is neglected. Is such a situation possible in reality?

Given:

t1 = 20 ° Celsius – initial water temperature;

t2 = 100 ° Celsius – boiling point of water;

s = 4200 J / (kg * C) – specific heat capacity of water;

g = 10 Newton / kilogram – acceleration of gravity.

It is required to determine h (meter) – from what height a drop of water should fall so that it boils when it hits the ground.

Since the condition of the problem is not specified, we assume that all the energy upon impact of the drop will go to its heating. Then, according to the law of conservation of energy:

Epotential = Q;

m * g * h = m * c * (t2 – t1), where m is the mass of the drop;

g * h = c * (t2 – t1);

h = c * (t2 – t1) / g = 4200 * (100 – 20) / 10 =

= 4200 * 80/10 = 4200 * 8 = 33600 meters = 33.6 km.

Answer: the drop must fall from a height of 33.6 kilometers (in reality, such a situation is impossible, since the air resistance force does not participate in solving the problem. In fact, falling from such a height, the drop will evaporate even before hitting the ground as a result of heating from work against the force of air resistance).