METEO 431: Atmospheric Thermodynamics
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1 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 concepts and how they are applied. If you are vague I assume that you do not understand a concept & deduct points! Please do not do a braindump in an attempt to stumble upon the right answer as you may end up saying something wrong! If a question is unclear to you then please ask. Good luck and do good work! 1. Short Answer: Answer each of the following in a maximum of 2-3 sentences. (a.) What is the difference between and ideal and a real gas? (b.) Why does van der Waal s equation predict a phase change? (c.) What is the enthalpy of sublimation? (d.) What relates changes in T to changes in internal energy? (e.) What is equilibrium vapor pressure?
2 2. An ideal gas is composed of 50% N 2, 30% O 2, and 20% H 2 O. Each m 3 of the gas weights 420 g. (a) What is the pressure exerted by this gas at T = 10C? (b) What is the total internal energy and the total enthalpy of 10 m 3 of this gas? (c) What is the total kinetic energy (internal) of 10 m 3 this gas?
3 3. During winter, cold air flowing southward out of Canada is advected over the relatively warm Great Lakes of the U.S. Assume that this cold air has a temperature of -20C and a presssure of 1000 mb. The lakes have a surface temperature of ~ 5C. (a) How much energy will it take to warm 10 kg of this air to the lake s temperature if the volume is constant? (b) Will the pressure increase, decrease, or stay the same during this heating? If it will increase or decrease, then calculate the pressure change. (c) Compute the specific, and total, entropy change of the parcel. (d) Calculte the specific entropy change of the lake.
4 4. On summer days, the lower 1 to 2 km of the Earth s atmosphere can undergo dry convective over-turning (i.e. parcels rise and then sink back to Earth in up and downdrafts). Assume a parcel is situated at 1 km above the surface of Denver, Colorado, with a pressure of 700 mb, a temperature of 15C, and an RH = 60%. (a) What is the potential temperature of this parcel? (b) If this parcel is brought back to the surface (850 mb), what temperature will it have? (c) What will be the parcel s RH at the surface? (d) How will the specific entropy of the parcel change due to the parcel s decent to earth?
5 5. In northern environments, it is typically better to use the frost point (T di ) rather than the dew point (T d ) temperature. The frost point is defined in the same way as the dew point except that the equilibrium vapor pressure with respect to ice is used. (a) Write down an expression for the frost point. (The dew point equation can be used as a guide.) (b) Do you expect T di to be greater than, equal to, or less than T d. Why? Be as quantitative as you can.
6 6. In order to cool down your warm drink, you take a few ice cubes from your freezer and toss them into your drink. (a) Does the ice completely melt? (b) How much does the drink cool down by the addition of the ice? Estimate this assuming: a glass with liquid that is 5 inches tall, and 3 inches in diameter; the liquid has a temperature of 50 F; you toss in 4 ice cubes that are 3cm long on each side; ice has a density of 900 kg/m 3 ; the specific heat of ice is 2106 J/kg; and that the initial ice temperature is 10F. (c) How much does the total entropy change during the melting of the ice?
7 Extra Credit: Do ONLY ONE problem. Extra Credit. (up to 10 pts) Rogers and Yau s, A Short Course in Cloud Physics, a famous undergraduate cloud physics text, explains latent heat in the following way: Heat is required to change phase from liquid to vapor because the kinetic energy of the vapor molecules exceeds that of liquid molecules at the same temperature. Please quantitatively demonstrate that this is rubbish. Extra Credit. (up to 10 pts) If you bend over and open the door of a hot oven to examine cooking food, and you are wearing glasses, your glasses may fog up. This seems to be at odds with the fact that in cold climates, where houses are heated during the winter, people tend to use humidifiers. Please explain.
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