Suppose 2.7 centimeters of rain at 15 degrees Celsius falls on a rectangular field of dimensions 2.1 kilometers by 1.1 kilometers. The amount of energy released when water vapor condensed and cooled to form this rain is equivalent to how many Hiroshima-size atomic bombs? One such bomb has an energy equivalent of about 6.3 x 1013 joules. Assume the water vapor condensed from its minimum possible temperature.

To solve this problem, we need to calculate the amount of energy released when water vapor condenses and cools to form rain. We can then compare this energy to the energy released by a Hiroshima-size atomic bomb.

First, let's calculate the volume of water that fell on the field. We have the depth of rain and the dimensions of the field.

Volume of Water (V) = Depth of Rain × Length × Width

Converting the depth of rain from centimeters to meters:
Depth of Rain (D) = 2.7 cm = 2.7/100 m

Length = 2.1 km = 2.1 × 1000 m
Width = 1.1 km = 1.1 × 1000 m

Now we can calculate the volume of water:
V = (2.7/100) m × (2.1 × 1000) m × (1.1 × 1000) m

Next, let's calculate the mass of the water using its density. The density of water is approximately 1000 kg/m³:

Mass (m) = Density × Volume

m = 1000 kg/m³ × V

We also need to find the change in temperature from the minimum temperature of the water vapor to 15°C. The specific heat capacity for water is approximately 4186 J/kg°C:

Temperature Change (ΔT) = Final Temperature - Initial Temperature
ΔT = 15°C - (-273.15°C) (Using the minimum possible temperature of water vapor, which is 0 Kelvin)

Now we can calculate the energy released when water vapor condenses and cools to form rain using the following formula:

Energy (E) = Mass × Specific Heat Capacity × Temperature Change

E = m × 4186 J/kg°C × ΔT

Finally, we can compare this energy with the energy released by one Hiroshima-size atomic bomb:

Energy of a Hiroshima-size atomic bomb = 6.3 × 10^13 J

To find the number of Hiroshima-size atomic bombs, we divide the energy released by the atomic bomb by the energy released by the condensation and cooling of water vapor:

Number of Atomic Bombs = E / (6.3 × 10^13 J)

By plugging in the calculated values and performing the calculations, we can find the number of Hiroshima-size atomic bombs equivalent to the energy released by the rain.