METEO 431: Atmospheric Thermodynamics

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Dominick Mitchell Shepherd
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1 METEO 431: Atmospheric Thermodynamics Example Test #1 (100 points) INSTRUCTIONS: Please write as legibly as you can and make sure your thoughts are organized. What I am looking for is your understanding of the key concepts and how they are applied. If you are vague I assume that you do not understand a concept & deduct points! Therefore, a few extra words that clarify your ideas are better than too few words. If a question is unclear to you, please ask. However, realize that I cannot give away answers. I can only help to reasonably clarify a question! Note that the last page contains a list of potentially useful constants. NOTE: THIS EXAMPLE IS LAST YEARS TEST PLUS TWO EXTRA QUESTIONS. SO THAT YOU CAN GET SOME EXTRA PRACTICE THINKING ABOUT THESE IDEAS. 1. (a) (5pts) Write down the equation of energy conservation for an air parcel. (b) (10 pts) Please provide a description of each term (there are 4 of them) in the equation. Please write no more than a few (3-4) sentences in your description of each term. (c) (10 pts) Energy conservation simply says that total energy won t change. It tells us nothing about how energy is transferred. How is energy transferred between objects with different temperatures? Page 1

2 2. While studying for this exam, you get incredibly frustrated and throw your Thermodynamics text high into the air. Assume that you were lying flat on your back, so that the book is only a very small distance above the ground when you release it. (a) (8pts) Assuming that the book s initial velocity is 10 m s -1, how high would the book go? Assume that the book weights 1 lb. (b) (8pts) The book comes crashing back to Earth, just missing your head. Neglecting any air drag on the book during its travels, how much energy does the book have when it reaches the ground? (c) (9 pts) The book hits the ground with a resounding thump. Ignoring sound, briefly describe the energy transfers that occur when the book contacts the ground. Page 2

3 3. Let s suppose you took a trip in your car going v car = 65 miles hr -1 and that you covered 100 km. During your trip, you experience head-winds of 10 m s -1 for the first half of your trip, and tail-winds of 10 m s -1 for the remainder of your trip. (a) (9 pts) How much energy (in Joules) does your car use during the trip? Recall that the equation for the drag force is F D = --ρ (each coefficient is given 1 2 a v 2 AC D on the last sheet.) Hint: The v in the drag force must be a combination of the car s and wind s velocity. (b) (8 pts) How much energy would you have used if there wasn t any wind? (c) (8pts) What do your results tell you about the influence of the wind on gas mileage? Page 3

4 4. In class we discussed the fact that: ext F i vi = Q + W i (a) (13 pts) By separating the velocity, and assuming that gravity is the only external force, please prove that the sum on the left hand side is equal to Mg, where M is the mass of the whole parcel. vcm (b) (12 pts) Is the result you derived in (a) a working term or a heating term? Why? Does gravity affect, K int, K cm, or both? Why? Page 4

5 5. Cars in Alaska have engine block heaters that allow you to plug your automobile into an electric outlet which keeps the battery and engine oil warm. Usually, one needs to plug her/his car in when the temperature is consistently below 10 F. On a particularly warm March day the temperature outside was 15F and I did not plug my car in at work. However, it was windy out (a rarity in Fairbanks) and so a well meaning friend of mine told me that I should go back and plug in my car because the weather service had said that the wind chill was -5F. Was my friend correct? Should I turn around and plug my car in? (Hint: You don t even need to know what wind chill is to answer this question!) Page 5

6 6. Consider the following situation: You place a kettle on the stove to make tea. You turn the stove on and in minutes the water starts boiling and the lid pops slightly off. Please use energy conservaton and energy transfer ideas to discuss (qualitatively) the processes that are occurring. Page 6

7 EXTRA CREDIT Extra Credit. (up to 10 pts) A high jumper s body goes over the top of a high bar during a jump. However, the jumper can go over the bar in such a way that her/his center of mass goes underneath the bar. Please explain. A sketch or two might help. Why would it be advantageous for a high jumper to use this technique? Page 7

METEO 431: Atmospheric Thermodynamics

METEO 431: Atmospheric Thermodynamics Final Exam (100 points) INSTRUCTIONS: Please write as legibly as you can and make sure your thoughts are organized. I am looking for your understanding of the key