Part #1: How much water and energy are in a small storm? (20 points)

The liquid water that is in a thunderstorm in the Midwest primarily comes from evaporated water from the Gulf of Mexico. When that water vapor condenses in the updraft of a thunderstorm, tiny liquid water droplets form and the storm is born. Let’s calculate how much water and energy is in a small thunderstorm complex – the kind that pop up on a hot summer day. Please find the total number of gallons of water in this storm and also the total energy content of the storm expressed in megatons and joules. You must show your work to get credit.

Assumptions:

Each cubic centimeter (cm3) contains 7.5*10-7 grams of water (7.5*10-7 g/cm3)

The storm’s dimensions are 20 km wide, 15 km long and 9 km tall.

1 gallon of water = 3785 grams of water

Each gram of water in the cloud releases 2260 Joules of energy as it forms those tiny cloud droplets (2260 J/g)

A 1-megaton nuclear bomb contains 4.18*1015 Joules of energy.

Water in the Atmosphere

Scenario: February is often a bitterly cold month and you may spend most of the month with a sore throat and cough. A doctor will recommend that you get a humidifier to help raise the humidity levels in your apartment. Before you turn on your humidifier, you decide to measure the relative humidity and air temperature in the room and find that the RH = 12.4% and the temperature is 68°F. Using this information answer the following questions. (Hint: check out figure 1.9 in the textbook and in the video lecture I provided***.)

- Write down the equation for relative humidity (RH) in the space below.

- What is the air temperature in Celsius?

- What is the saturation vapor pressure (SVP) of the air in your apartment?

- What is the vapor pressure (VP) of the air in your apartment?

- What is the dewpoint temperature (Td) of the air in your apartment?

Six hours after turning your humidifier on, you measure the humidity levels again and see that the relative humidity has risen to 50% and you are now finding some relief in your sore throat and your cough is gone. The air temperature has not changed. Answer the following questions.

- What is the dewpoint temperature in your apartment now that the RH is 50%?

- What is the vapor pressure (VP) of the air in your apartment now?

- What is the saturation vapor pressure (SVP) of the air in your room now?

- If you were to raise the air temperature in your room to 72°F, how would this change the relative humidity (increase, decrease or stay the same)? In one or two sentences, explain your answer.

*** Figure 1.9 shows the relationship between the SVP and Temperature. If you know the air temperature (in Celsius) you can find the SVP (in mb). This same chart can be used to find the vapor pressure (VP) if you know the dewpoint temperature (Td). This works because when the relative humidity is 100%, the VP = SVP and T = Td. So, as you are trying to answer questions #4 and #7 above, use Figure 1.9 to find the VP.