Handouts
LINK: THERMODYNANIC SYSTEMS AND IDEAL GAS LAW
Topics:
First Law of Thermodynamics
Thermodynamic System
Bernoulli's Principle
Properties of Pure Substance
General Gas Law
Exercises
|
1. A 4 kg/s of fluid enters a device with an initial pressure of 700 kPa, initial velocity of 70 m/s and the fluid initial fluid density of 3.0 kg/m3. The fluid leaves the device at 182 kPa, 150 m/s and 0.80 kg/m3. The heat loss from the device is 19 kJ/kg and the work done by the fluid is 232 kW. Determine the change in internal energy. b. -65.32 kJ/kg c. -58.32 kJ/kg d. -48.33 kJ/kg 2. A fluid enters an apparatus at 480 ft/sec, initially, the pressure of the fluid is 120 psia, the specific volume of 5 ft3/lb and the internal energy is 383 Btu/lbm. The fluid leaves the apparatus at 25 psia, specific volume of 18 ft3/lbm, an exit velocity of 1200 ft/s and internal energy of 120 Btu/lbm. The heat radiation loss is 10 Btu/lbm. Determine work steady flow, WSF. a. 351.4 Btu/lbm c. 428.5 Btu/lbm d. 282.8 Btu/lbm 3. A gas is contained in a 0.5 m3 rigid tank. The gas receives a paddle work of 5.5 W for 30 minutes. At initial state, the density of the gas is 1.8 kg/m3. Determine the change in specific internal energy in kJ/kg. a. 10 kJ/kg b. 11 kJ/kg c. 12 kJ/kg d. 13 kJ/kg 4. 8 kg of steam is contained a piston-cylinder as shown in the figure below, 75 kJ of heat is transferred to the steam causing it to expand from initial state where the specific internal energy is u1=2710.0 kJ/kg to final state where u2 = 2660.5 kJ/kg. During the process, a 20 kJ of paddle wheel work is also added to the steam. Assuming that there is no significant change in kinetic and potential energies, determine the work transferred by steam to the piston during the process, in kJ.
a. 430 kJ b. 452 kJ c. 520 kJ d. 491 kJ 5. A gas is contained in a piston-cylinder arrangement, energy is added in such a way that the quantity PV remains constant. The initial pressure of the gas is 250 kPa and the initial volume is 2 m3. If the final pressure is 120 kPa. Calculate the work done by the gas on the piston. a. 367 kJ b. 352 kJ c. 330 kJ d. 401 kJ 6. A piston-cylinder shown below is connected with a paddle wheel coupled in a 120 kg mass. The mass drops 4 meters, causing the piston to increase by 0.0025 m3. If the weight and the piston maintain a constant pressure of 100 kPa, determine the net work done by the gas on the piston. Neglect friction between the piston and the cylinder surface.
a. -6.46 b. -3.46 kJ c. -4.46 kJ d. -5.46 kJ 7. 1.8 kg/s of steam expands in a turbine producing 550 kW of power output. The steam enters at a velocity of 18 m/s and exits at 70 m/s. The reduction of specific enthalpy is 400 kJ/kg. Determine the heat flow per second when the inlet of the turbine is located 900 mm above the outlet. a. 152.8 kW b. 160.3 kW c. -165.9 kW d. -170.1 kJ 8. A well-insulated and perfectly sealed room is installed with 4-hp fan to circulate air for 1.5 hours. Determine the increase in internal energy of the air. a. 4.11x107 J b. 3.32x107 J c. 1.61x107 J d. 2.21x107 J 9. A rigid container with a volume of 8ft3 contains steam with an initial specific volume of 1.2851 ft3/lbm and initial internal energy of 1150 Btu/lbm. Determine the final internal energy, in Btu/lbm if 800 Btu is added in the system. a. 1278.51 b. 1352.11 c. 1558.22 d. 1628.62 10. Steam flowing at a rate of 3200 lbm/hr enters an adiabatic nozzle. The initial condition of steam is: P1 = 250 psi, v1=620 ft/min, 2.4 ft3/lbm and u1 = 1125.5 Btu/lbm. The steam exits at: P2 = 35 psi, 18.5 ft3/lbm and u2 = 985 Btu/lbm. Determine the exit velocity of the steam in ft/sec. a. 3058.11 b. 2017.88 d. 3681.88 11. An ideal gas with a mass of 2 kgs is contained in a 3.2 m3 rigid container. The initial temperature is 303 K and a pressure of 150 kPa. Determine the ideal gas constant. a. 0.7921 b. 0.8121 c. 0.6112 d. 0.5033 12. A rigid tank initially contains hydrogen initially at 100 kPa and 20oC. One and a half kilograms of hydrogen is added so that the final temperature and pressure of the tank is 30oC and 250 kPa, respectively. Determine the volume of the tank, in m3 and the final mass of the hydrogen inside the tank, in kgs. a. 12.8 and 3.66 b. 16.1 and 4.21 c. 11.7 and 1.10 d. 12.8 and 2.56 13. A pressurized vessel contains air at a gage pressure of 275 kPag and temperature of 28oC. If the bursting gage pressure of the vessel is found to be 1800 kPag, determine the temperature where the vessel will burst, in oC. a. 1247.8 b. 2012.1 c. 1320.8 d. 1822.2 14. A 2-m3 rigid vessel contains helium initially at a gage pressure and temperature of 320 kPa and 315 K, respectively. Because of the leaks in the fittings of the vessel, the gage pressure dropped to 280 kPa and the temperature decreased to 300 K, determine the mass of the helium that leaked out and also the mass of nitrogen that remained in the vessel, in kg. a. 0.03211 and 1.8821 kg b. 0.06399 and 1.2240 kg c. 0.05312 and 1.5120 kg d. 0.06112 and 1.7211 kg 15. Two closed vessel A and B contains air and is connected together by a valve. Vessel A has a volume of 90-L at 3500 kPa and 60oC, while vessel B has an unknown volume at 200 kPa and 20oC. After a while, the valve was opened and the resulting pressure and temperature of the mixture are 1800 kPa and 32oC, respectively. Determine the volume of vessel B, in L. a. 65.3 L b. 79.5 L c. 84.5 L d. 75.2 L 16. 0.1 kg of air is contained in a spring-loaded piston-cylinder arrangement as shown in the figure below. The mass of the piston is 80 kg with a diameter of 20 cm. The piston is exposed to an atmospheric pressure of 101 kPa. Initially, the temperature of air is 300 K and the spring just touches the top of the piston. Heat is added until the spring is compressed to 18.0 cm. Neglect the effect of friction between the piston and cylinder and let the spring constant to be 30 kN/m. Determine: The initial pressure, in kPa and final temperature, in K of air inside the cylinder.
a. 126 kPa and 768 K b. 132 kPa and 800 K c. 126 kPa and 820 K d. 132 kPa and 770 K 17. Air enters an electric furnace at 100 kPa and 28oC with a volume flow rate of 22 m3/min. At the exit of the furnace, the air is 100 kPa and 50oC. The air passes through a ducting system consisting of three branches, one duct with 30cm diameter and the other two with 16cm diameter. If the velocity of air in the 16cm ducting was measured to be 3.7 m/s, determine the mass flow rate, in kg/s of air entering the furnace and the velocity in m/s of air in the 30 cm duct. a. 0.5233 kg/s and 4.44 m/s b. 0.3421 kg/s and 3.21 m/s c. 0.4244 kg/s and 3.46 m/s d. 0.3321 kg/s and 2.28 m/s 18. A vertical piston cylinder arrangement shown below with a piston mass of 60 kg with a face area of 150 cm2, contains 5 grams of air. The initial volume occupied by the air is 6L. A heat loss of 2.0 kJ occurs because of the temperature difference between the surroundings and volume inside the cylinder that caused the volume to decrease by 3L. The atmospheric pressure at the top of the piston is 101 kPa. Neglect the friction effects between the surface of the piston and the cylinder. Determine the change in internal energy of air, in kJ/kg. a. -484.14 b. -525.12 c. -315.86 d. -493.10 |
Open or Steady Flow System
Air flows steadily at a rate of 0.6 kg/s through an air compressor, entering at 8 m/s speed, 120 kPa and 0.90 m3/kg specific volume and leaving at 6 m/s, 700 kPa and 0.20 m3/kg. The change in internal energy of the air is 98 kJ/kg. Cooling water in the compressor jacket absorbs heat from the air at the rate of 50 kJ/s. Compute for the power needed by the compressor, in kW.
SOLUTION:
Nozzle Open System
Compressed air with negligible velocity and temperature at 35 deg C enters a nozzle. At the exit to the nozzle the pressure is 100 kPa but the velocity is 200 m/s. Calculate the temperature of the air at the exit, assuming Cp of air equal to 1.00 kJ/kg-K.
SOLUTION:
Ideal Gas Laws
Nitrogen is contained in 0.18 m3 tank and the initial pressure and temperature is 110 kPa and 18 deg C. Determine: (a) the mass of the gas, in kg (b) The final pressure of the gas remaining in the tank, in kPa if 0.2 kg of gas leaks out of the tank and in the process the temperature drops to 33 deg C. Let the atmospheric pressure to be 100 kPa.
SOLUTION:
