Mechanical Engineering 300 – Engineering Thermodynamics I

 

Sections 1 and 3                                                      Spring Semester 2008

 

Homework 3                                                                Due Monday February 18, 2008 

 

1. A 0.5-m3 vessel contains 10 kg of refrigerant-134a at -20 °C.  Determine (a) the pressure, (b) the total internal energy, and (c) the mass of each phase. 

(a) 133 kPa, (b) 890 kJ, (c) 0.00487 m3  (C&B)

Is the answer to part b a relative quantity or an absolute quantity?

 

 

2. The pressure in an automobile tire depends on the temperature of the air in the tire.  When the air temperature is 25 °C, the pressure gage reads 210 kPa.  If the volume of the tire is 0.025 m3, determine the pressure rise in the tire when the air temperature in the tire rises to 50 °C.  Also determine the amount of air that must be bled off to restore the pressure to its original value at this temperature.  Assume that the atmospheric pressure is 100 kPa.   6.95 g air (C&B)

 

 

3. Determine the specific volume of superheated water vapor at 10 MPa and 400 °C, using (a) the ideal-gas equation and (b) the property tables.  Calculate the percent error.

 

 

4. During a hot summer day at the beach when the air temperature is 30 °C, someone claims the vapor pressure in the air to be 5.2 kPa.  Is this claim reasonable?  (C&B)

 

 

5. Solve the following problems from S. R. Turns, "Thermodynamics: Concepts and Applications."

 

2.33

 

2.37                        

 

4.7                         

 

4.12                      

 

 

6. Although balloons have been around since 1783 when the first balloon took to the skies in France, a real breakthrough in ballooning occurred in 1960 with the design of the modern hot-air balloon fueled  by inexpensive propane and constructed of lightweight nylon fabric.  Over the years, ballooning has become a sport and a hobby for many people around the world.  Unlike balloons filled with the light helium gas, hot-air balloons are open to the atmosphere.  Therefore, the pressure in the balloon is always the same as the local atmospheric pressure, and the balloon is never in danger of exploding.

 

Hot-air balloons range from about 15 to 25 m in diameter.  The air in the balloon cavity is heated by a propane burner located at the top of the passenger cage.  The flames from the burner that shoot into the balloon heat the air in the balloon cavity, raising the air temperature at the top of the balloon from 65 °C to over 120 °C.  The air temperature is maintained at the desired levels by periodically firing the propane burner.  The buoyancy force that pushes the balloon upward is proportional to the density of the cooler air outside the balloon and the volume of the balloon, and can be expressed as

 

                             FB =   rcool air gVballoon

 

where g is the gravitational acceleration.  When air resistance is negligible, the buoyancy force is opposed by (1) the weight of the hot air in the balloon, (2) the weight of the cage, the ropes, and the balloon material, and (3) the weight of the people and other load in the cage.  The operator of the balloon can control the height and the vertical motion of the balloon by firing the burner or by letting some hot air in the balloon escape, to be relaced by cooler air.  The forward motion of the balloon is provided by the winds. 

 

Consider a 20-m-diameter hot-air balloon that, together with its cage, has a mass of 80 kg when empty.  This balloon is hanging still in the air at a location where the atmospheric pressure and temperature are 90 kPa and 15 °C, respectively, while carrying three 65-kg people.  Determine the average temperature of the air in the balloon.  What would your response be if the atmospheric air temperature were 30 °C?   Thot = 323.5 K    (C&B)

 

 

 

"(C&A)" indicates a problem taken from Y. A. çengel and M. A. Boles, "Thermodynamics – An Engineering Approach," fifth edition.