Homework Assignments Answers

First & last name: ______________________________ Homework Assignment #1 - Answers ATOC 181, Winter 2014 Assigned: 16th January 2014 Due: 23rd January 2014 • Provide hand-written or typed answers to the following questions (max. 10 points per numbered block of questions). • Submit a (stapled) hard copy of your answers at the beginning of class on the due date or before. • Make sure that your first and last name are stated at the top right corner of the answer sheets. • Each sub-question should be answered concisely in 1-3 sentences (state the key points). 1. List the dominant heat-transfer mechanism (among conduction, convection, advection, and radiation) in the following five situations and briefly explain your logic for each choice: a) The Earth’s surface is heated by sunshine during a summer day. Radiation: the surface absorbs incident shortwave (solar) radiation and gains energy. b) Warm air from the Gulf of Mexico overspreads southeastern Canada in southerly winds. Advection: air is transported horizontally from a warm to a cold region. c) In the long-lasting darkness of arctic winter, the polar region becomes increasingly cold. Radiation: continuous emission of terrestrial (longwave / infrared) radiation without any solar heating results in a net loss of heat. d) The air layer in contact with the Earth’s surface heats up on a sunny day with no wind. Conduction: heat is transferred by molecular collisions across the interface from the ground to the first mm of air at the surface. e) Turbulent eddies mix hot air just above the surface with ambient air aloft. Convection: heat is transferred by buoyant motions (rising warm air and sinking cold air). 2. Situation: suppose you cooked a pasta dish for dinner that you top with a sauce containing large chunks of tomatoes. Both the pasta and the sauce had been brought to boiling temperature for a few minutes until ready to eat. You then arrange the steaming hot pasta Page 1 of 3 with sauce on a plate, let it rest for a minute and then start eating. Based on this situation, answer the following questions using physical reasoning. a) As you start eating, you realize that the tomato chunks are still very hot; warmer than the pasta. Explain why. The key point here is the high specific heat capacity (specific heat) of water in comparison to other substances, such as cooked pasta. The tomato chunks contain mainly water, the pasta less water. The pasta cools off more quickly due to evaporation of hot water from its surface and less water content (also thinner). The high heat capacity of water in the tomato chunks requires a larger amount of heat to be transferred from the tomatoes to the surrounding air; therefore, they cool off slower. b) If the pasta and the tomato chunks were to represent the thermal properties of a large lake and of a volume of wet soil, which one would be the lake? The tomato chunks would represent the lake (again, heat capacity of water is the thermal property that is important here). A large lake will have a higher specific heat capacity than wet soil (cooling / warming slower and reducing local climate extremes). 3. Answer the following three questions about greenhouses gases: a) How does their electromagnetic absorption depend on the wavelength of the radiation? These gases tend to predominantly absorb longwave (infrared) electromagnetic waves but not shortwave (visible) radiation. b) Why are these gases important for the global climate? They absorb longwave (or “terrestrial”) radiation emitted by the Earth and radiate part of it back down, causing the Earth (surface) to receive more radiant energy and become warmer. As a consequence, the global average air temperature is sensitive to the concentrations of these gases. c) Why are water vapor and carbon dioxide (CO2) considered to be the two most important greenhouse gases? Like all greenhouse gases, H2O and CO2 absorb and emit large amounts of infrared radiation, causing a heating of the earth. These are by far the two most abundant greenhouse gases, making them the most important. Other greenhouse gases are more efficient absorbers per unit mass (global warming potential) but they tend to be present in much lower concentration. 4. Answer the following questions about the vertical structure and composition of the atmosphere. a) Ozone is found in the surface air of the troposphere as well as in the stratosphere. Why is it considered “good ozone” in one of the layers and “bad ozone” in the other? Ozone is considered as “good” in the stratosphere (ozone layer) due to its important role as an efficient absorber of solar UV radiation, protecting life on the surface. Ozone in the surface air is considered “bad” as it is a major Page 2 of 3 component of photochemical smog (air pollution), affecting the health of humans. b) In the atmosphere both air pressure and density decrease exponentially with height. A similar vertical profile in the oceans shows that density does change only very little from the surface down to the ocean floor (practically staying constant in comparison to the large vertical change in the atmosphere). What physical property of air in comparison to liquid water explains the different vertical density profiles? Air is a mixture of gases and gases are compressible (water, as most liquids and solids, is nearly incompressible). Therefore, under the influence of Earth’s gravity and the overlying mass in a column of air, the density increases from high altitude toward the surface. This level of compression is not possible in a column of liquid water. c) Qualitatively, how will the pressure change in the ocean profile with depth? (Hint: recall what pressure represents in the atmosphere at a certain altitude.) Pressure in a column of air or water essentially represents the weight of the overlaying air/water column. In the ocean, the pressure will increase approximately linearly with increasing depth. The reason is that the water density is practically constant in the vertical, so the pressure increases linearly as more and more water (of equal density) is overhead with increasing depth. Page 3 of 3

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Late penalties | How grading works | When to guess and when not to guess | When to answer using radians or degrees

 

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