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When water vapor transforms into liquid water, it releases energy in the form of latent heat. This heat, known in physics as the latent heat of vaporization, is the energy necessary to convert water from a gaseous state to a liquid state without changing its temperature. For water, this value is a substantial 2.26 million joules per kilogram (J/kg).
The importance of latent heat is immense, especially when considering large-scale natural processes like rainfall. As rain falls, it involves a massive amount of water condensing from vapor, and thus, releases significant energy into the environment. By understanding this concept, we can appreciate how natural phenomena impact our energy systems.
In the problem, the energy released during the condensation process when rain falls over an area is calculated using the formula:\[E = m \times \text{Latent Heat of Vaporization}\]where \(m\) represents the mass of the rain in kilograms. This relationship shows the direct proportionality between mass and energy released.

Estimating the mass of rain is a straightforward process that uses the volume of rain and the density of water. Given that the density of water is typically about 1000 kilograms per cubic meter (kg/m³), we can find the mass of water with the formula:\[m = \text{Volume} \times \text{Density}\]Here, the mass \(m\) is determined by multiplying the volume of the rainfall (in cubic meters) with the density of water.
Understanding the mass of rain is crucial, as it’s directly related to the calculation of energy released during condensation. Mass represents how much water is involved in the rainfall, which in this exercise, comes out as 65.8 million kilograms. This demonstrates the enormous scale of water movement during such weather events.
The concept of mass of rain also underscores the efficiency of natural processes at redistributing water and energy across vast geographic areas efficiently and sustainably.

To determine how much rain fell over an area, one must calculate the volume. This is simply the product of the height of the precipitation and the area over which it falls. The formula is expressed as:\[V = \text{Height of Rain} \times \text{Area}\]For the given problem, rain with a specific height falls over a defined area — much like how a thin layer of water covers a large surface.
Calculating the volume of rain is an important first step, as it sets the foundation for determining the mass and consequently the energy released. It allows us to shift from an abstract idea of precipitation to quantifiable measures that connect to broader environmental and meteorological concepts.
By measuring the volume, we find the scale of the water involved in rainfall events. In this exercise, the computed volume of rain is 65,800 cubic meters. This highlights the impressive scale of natural water cycles and reinforces the interconnected concepts of volume and mass.