Question

During a hailstorm, it was observed that ice pieces turned into water when they reached the ground. At what height would the raindrop have formed from ice pieces?
a) $33.44$ Km
b) $300$ Km
c) $33$ Km
d) $30$ Km

Answer 1

When matter changes state, 'latent heat' assists in 'splitting the bonds' at the transition state, and Latent heat is the energy released or consumed during a fixed temperature phase change. However, energy can neither be formed nor destroyed. So, considering that, latent heat has to transform into some form of energy.

Complete step-by-step solution:
During a hailstorm, it was observed that ice pieces turn into water. So, the heat required to melt ice is given by:
$Q = mL$
Q is the required heat.
m is the mass of ice.
L is the latent heat of melting.
Ice pieces dropped from a height. So, potential energy comes into play.
Potential energy $= mgh$
g is the gravity.
h is the height.
We need to calculate the height at which the raindrop has formed from ice pieces.
We will use the concept of conservation of energy. Potential energy will be equal to the heat for melting the ice.
$mL = mgh$
$\implies h = \dfrac{L}{g}$
We know, $L = 8 \times 10^{4} \times 4.18 J Kg^{-1}$
$g = 10 ms^{-2}$
Now put these values in the above formula:
$h = \dfrac{8 \times 10^{4} \times 4.18}{10}$
$\implies h = 33.44 Km$
Option (a) is right.

Note: Heat received or released as the outcome of a phase change is termed latent heat. There is no temperature difference during a phase transition. Thus, there is no variation in the kinetic energy of the particles in the substance. Instead, the energy liberated comes from the potential energy stored in the bonds among the particles.