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PS1 Solutions

# PS1 Solutions - 105A Introduction to Engineering...

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Unformatted text preview: , 105A Introduction to Engineering Thermodynamics Winter 2008 Problem Set I . Balloons are sometimes ﬁlled with helium gas because it has a mass only about one-seventh that of air under identical conditions. The buoyancy force, which may be expressed as F b = pair g Vbanoon, will push the balloon upward. If the balloon has a diameter of 10 m and carries two people having a mass of 70 kg each and the mass of the gondola is 64 kg, determine the acceleration of the balloon when it is ﬁrst released. Assume that the density of the air is pair = 1.16 kg/m3, and neglect the weight of the ropes and the balloon envelope fabric in your analysis. . ' . Express each of the following temperatures below in 0C, 0F, K, and CR: (a) Boiling temperature of water at sea level, 100°C. (b) Freezing temperature of water at sea level, 32°F (c) A winter temperature in Canada of -40°C. (d) Temperature of the sun, 57 80 K. . Hoover Dam, also known as Boulder Dam, is a concrete dam in the Black Canyon of the Colorado River, on the border between the U.S. states of Arizona and Nevada. The dam, located 30 miles (48 km) southeast of Las Vegas, is named after Herbert Hoover, who played an instrumental role in'its construction, ﬁrstas Secretary of Commerce and then later as President of the United States. Seventeen turbine-generators at this powerhouse generate a maximum of 2,080 MW of hydroelectric power of which about 60 percent is allocated for use in Southern California. The dam is 221 m high, 379 m long, and has a thickness of 200 m at its base and 15 m at its crest. Estimate the maximum pressure in kPa that this dam must withstand. [Problem 2.7 in Moran & Shapiro] A 30-seat turboprop airliner whose mass is 14,000 kg I takes off from an airport and eventually achieves its cruising speed of 620 km/h at an altitude of 10,000 m. For g : 9.78 III/32, determine the change in kinetic energy and the change in gravitational potential energy of the airliner, each in 1d. 5. A gas expands from an initial state where p1 : 500 kPa and V1 = 0.1 m3 to a ﬁnal state where p; : 100 kPa. The relationship between pressure and volume during the process is pV : constant. Sketch the process on a p—V diagram and determine the work, in k]. 6. [Problem 2.31 in Moran & Shapiro] Warm-air is contained in a piston-cylinder assembly oriented horizontally as shown in Fig. P231. The air cools slowly from an initial volume of 0.003 m3 to a ﬁnal volume of 0.002 n13. During the process, the spring exerts a force that varies linearly from an initial value of 900 N to a ﬁnal value of zero. The atmospheric pressure is 100 kPa, and the area of the piston is 0.018 mg. Friction between the piston and cylinder can be neglected. For the air, determine the initial and ﬁnal pressure, in kPa, and the work, in k]. Due Tuesday, January 15, 2008. /. 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PS1 Solutions - 105A Introduction to Engineering...

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