Question

Explain why thunderstorms are more likely in the summer than in the fall during rainstorms, after calculating the energy released under each condition.   Assume a summer temperature of 90°F and fall 40°F and that the rain is 40°F. Note that the specific heat of water is 4.184 J/g-˚C, and that the heat of vaporization of water is 2600 J/g.

Answer 1

Answer 2

Thunderstorms are more likely in the summer than in the fall during rainstorms due to the higher energy available in the atmosphere during the summer. Thunderstorms are caused by the rapid upward movement of warm, moist air that then cools and condenses to form clouds. This process releases energy, which can then lead to thunder and lightning.

To illustrate this point, we can calculate the energy released under each condition given the specific heat of water and the heat of vaporization of water. The energy released in a thunderstorm is related to the amount of moisture in the air and the temperature difference between the air and the surrounding environment.

Let's consider the energy released in a thunderstorm in the summer and the fall.

In the summer, assume that the air temperature is 90°F (32.2°C) and the rain temperature is 40°F (4.4°C). The temperature difference is 32.2°C - 4.4°C = 27.8°C.

Using the specific heat of water, we can calculate the amount of energy released when 1 g of water cools from 32.2°C to 4.4°C:

Energy released = mass x specific heat x temperature difference Energy released = 1 g x 4.184 J/g-˚C x 27.8°C Energy released = 116.5 J

Next, we can calculate the amount of energy released when 1 g of water vapor condenses to form liquid water at 40°F (4.4°C):

Energy released = mass x heat of vaporization Energy released = 1 g x 2600 J/g Energy released = 2600 J

Therefore, the total energy released when 1 g of water vapor condenses in the summer is:

Total energy released = energy released from cooling + energy released from condensation Total energy released = 116.5 J + 2600 J Total energy released = 2716.5 J

Now let's consider the same situation in the fall, with an air temperature of 40°F (4.4°C) and rain temperature of 40°F (4.4°C). The temperature difference is 0°C.

Using the specific heat of water, we can calculate the amount of energy released when 1 g of water cools from 4.4°C to 4.4°C:

Energy released = mass x specific heat x temperature difference Energy released = 1 g x 4.184 J/g-˚C x 0°C Energy released = 0 J

The amount of energy released when 1 g of water vapor condenses to form liquid water at 40°F (4.4°C) is still 2600 J.

Therefore, the total energy released when 1 g of water vapor condenses in the fall is:

Total energy released = energy released from cooling + energy released from condensation Total energy released = 0 J + 2600 J Total energy released = 2600 J

Comparing the total energy released in the summer and the fall, we can see that it is much greater in the summer. This is because there is a larger temperature difference between the warm, moist air and the cool rain, resulting in more energy being released when the water vapor condenses. Therefore, thunderstorms are more likely to occur in the summer than in the fall during rainstorms.