Homework 1
Earth’s Atmosphere and Climate
ENVST-UA0360 - MATH-UA0228
Due: Wednesday, February 5th
The homework focuses on Chapter 1 and the equation of state. Show how you obtained your answer. You only need to get numerical answers with 2-digit accuracy. Please submit it through Brightspace.
1. (10pt) [As the Superbowl is around the corner...] An unnamed team inflated their football to 15 psi (pounds per square inch) in a warm locker room (T = 20。C). Determine the pressure inside the ball when playing at near-freezing temperature (T = 0。C), assuming that the volume of the ball remains the same and no air has leaked out. [psi - pounds per square inch - is one of these old measuring units - only used nowadays for pressure in tires and footballs. You can solve this problem without converting to Pascal.]
2. (10pt) Compare the boiling point of water in Denver (air pressure is P = 8.3 × 104 Pa) and New York City (air pressure P = 105 Pa). Water boils when its saturation vapor pressure is equal to or greater than the atmospheric pressure, allowing for the formation of steam bubbles in the liquid.
3. (10pt) Compare the density of a parcel of dry air at a temperature of 200。C and pressure of 105 Pa, and a parcel of moist air at the same temperature and pressure, if the air contains 15 grams of water vapor per kilo of dry air.
4. (20pt) Compute the amount of water vapor (in grams per kilo of air) in a saturated air parcel at a temperature of 27。C and pressure of 105 Pa (this would be near the Earth’s surface in a tropical region) and in a saturated air parcel at a temperature of −70。C and a pressure of 2 × 104 Pa (This corresponds roughly to the top of a tropical thunderstorm, reaching 16 km in the atmosphere...). [An air parcel is saturated if the partial pressure of the water vapor is equal to the saturation vapor pressure (as given by eq. 1.4 in Marshall and Plumb) at that temperature.]