Engineering-thermodynamics

ENGINEERING THERMODYNAMICS 1. What is the weight of a 66-kgm man at standard condition?

66 kgf

2. The weight of an object is 50 lb. what is its mass at standard condition?

50 lbm 2

3. Five masses in a region where the acceleration due to gravity is 30.5 ft/s are as follow: m1 is 500 g of mass; m2 weighs 800 gf; m3 weighs 15 poundal; m4 weighs 3 lbf; m5 is 0.10 slug of mass. What is the total mass expressed (a) in grams, (b) in pounds, and (c) in slugs. 4. Note that the gravity acceleration at equatorial sea level is g=32.088 fps 2 per 1000 ft ascent. Find the height in miles above the point for which (a) the gravity acceleration becomes 30.504 fps2, (b) the weight of a given man is decreased by 5%, (c) what is the weight of a 180 lbm man atop the 29,131 ft Mt. Everest in Tibet, relative to this point. 5. Two liquids of different densities (ρ1=1500 kg/m3, ρ2=500 kg/m3) are poured together into a 100 L tank, filling it. If the resulting density of the mixture is 800 kg/m3, find the respective quantities of liquids used. Also, find the weight of the mixture; local g=9.675 mps2. 6. A vertical column of water will be supported to what height by standard atmospheric pressure. 7. The pressure of a boiler is 9.5 kg/cm2. The barometric pressure of the atmosphere is 768 mm Hg. Find the absolute pressure in the boiler. 8. A pressure gage registers 40 psig in a region where the barometer us 14.5 psia. Find the absolute pressure in psia, and in kPa. 9. Given the barometric pressure of 14.7 psia (29.92 in. Hg abs), make these conversions: a. 80 psig to psia and to atmosphere b. 20 in. Hg vacuum to in. Hg abs and to psia c. 10 psia to psi vacuum and to Pa d. 15 in. Hg gage to psia, to torrs, and to Pa 10. Two gaseous streams enter a combining tube and leave as a single mixture. These data apply at the entrance section: For one gas, A1=75 in2, v=500 fps, ν=10 ft3/lb For the other gas, A2=50 in2, m2=16.67 lb/s, ρ2=0.12 lb/ft3 At exit, v=350 fps, v3=7ft3/lb. Find: a. the speed v2(fps) at section 2, and b. the flow and area at the exit section. 11. A 10-ft diameter by 15-ft height vertical tank is receiving water (ρ=62.1 lb/cu.ft) at the rate of 300 gpm and is discharging through a 6-in ID line with a constant speed of 5 fps. At a given instant, the tank is half-full. Find the water level and the mass change in the tank 15 min. later. 12. What is the mass in grams and the weight in dynes and in gram-force of 12 oz of salt? Local g is 9.65 m/s2. 1lbm=16 oz. 13. A mass of 0.10 slug in space is subjected to an external vertical force of 4lb. If the local gravity acceleration is g=30.5 fps2 and if friction effects are neglected, determine the acceleration of the mass if the external vertical force is acting (a) upward and (b) downward 14. The mass of a given airplane at sea level (g=32.1 fps2) is 10 tons. Find its mass in lb, slugs, and kg and its (gravitational) weight in lb when it is travelling at a 50000 ft elevation. The acceleration of gravity g decreases 3.33x10 -6 fps2 for each foot of elevation. 15. A lunar excursion module (LEM) weights 1500 kgf on earth where g=9.75 mps 2. What will be its weight on the surface of the moon where gm=1.70 mps 2. On the surface of the moon, what will be the force in kgf and in Newton required to accelerate the module at 10 mps2? 16. The mass of a fluid system is 0.311 slug, its density is 30 lb/ft3 and g is 31.90 fps2. Find (a) the specific volume, (b) the specific weight, and (c) the total volume. 17. A cylindrical drum (2ft diameter, 3 ft height) is filled with a fluid whose density is

4461.07 gm 9.83 lbm 0.306 slugs 528000 ft or 100 miles 30.484 fps2 179.03 lbf 45 kg 35 kg 78.93 kgf 33.9 ft 10.54 kg/cm2 54.5 psia 375.78 kPa 94.7 psia, 5.44 atm 9.92 in. Hg abs, 4.87 [si 4.7 psi vacuum, 32407 Pa 44.92 in. Hg. 381 torrs, 50780 Pa(gage)

400 fps 42.71 lb/s 0.8542 ft2

3.91 ft 340.2 gm 328,300 dynes 334.8 gf 9.5 fps2 70.5 fps2 20,000 lbm 621.62 slugs 19850 lbf 261.5 kgf 1538.5 kgf 15087 N 0.0333 ft3/lb 29.75 lb/ft3 0.3335 ft3 9.43 ft3

40 lb/ft3. Determine (a) the total volume of fluid, (b) its total mass in pounds and slugs, (c) its specific volume, and (d) its specific weight where g=31.90 fps 2. 18. A weatherman carried aneroid barometer from the ground floor to his office atop he Sears Tower in Chicago. On the ground level, the barometer read 28.607 in. Hg absolute. Assume that the average atmospheric air density was 0.075 lb/ft3 and estimate the height of the building. 19. A vacuum gauge mounted on a condenser reads 0.66 m Hg. What is the absolute pressure in the condenser in kPa when the atmospheric pressure is 101.3 kPa? 20. Convert the following readings of pressure to kPa absolute, assuming that the barometer reads 760 mm Hg: a. 90 cm Hg gage b. 40 cm Hg vacuum c. 100 psig d. 8 in Hg vacuum, and e. 76 in. Hg gage 21. A fluid moves in a steady flow manner between two sections in a flow line. At sections 1: A1=10ft2, u1=100 fpm, v1=4ft3/lb. at section 2: A2=2ft2, ρ2=0.20 lb/ft3. Calculate: a. The mass flow rate b. The speed at section 2 22. If a pump discharges 75 gpm of water whose specific weight is 61.5 lb/ft3 (g=31.95 fps2), find: a. The mass flow rate in lb/min b. The total time required to fill a vertical cylinder tank 10 ft in diameter and 12 ft high. 23. During a steady flow process, the pressure of the working substance drops from 200 to 20 psia, the speed increases from 200 to 1000 fps, the internal energy of the open system decreases 25 Btu/lb, and the specific volume increases from 1 to 8 ft3/lb. no heat is transferred. Determine the work per lb. is it done on or by the substance? Determine the work in Hp for 10 lb per min. 24. Steam is supplied to a fully loaded 100 Hp turbine at 200 psia with u1=1163.3 BTU/lb, v1=2.65 ft3/lb and v1=400 fps. Exhaust is at 1 psia with u2=925 BTU/lb, v2=294 ft3/lb and v2=1100 fps. The heat loss from the steam in the turbine is 10 BTU/lb. neglect potential energy change and determine: a. The work per lb steam b. The steam flow rate in lb/hr 25. An air compressor (an open system) receives 272 kg per min of air at 99.29 kPa and a specific volume of 0.026 m3/kg. the air flows steady through the compressor and is discharged at 689.5 kPa and 0.0051 m3/kg. The initial internal energy of the air is 1594 J/kg; at discharge, the internal energy is 6241 J/kg. the cooling water circulated around the cylinder carries away 4383 J/kg of air. The change in kinetic energy is 986 J/kg increase. Compute the work. 26. A centrifugal pump operating under steady flow conditions delivers 2270 kg/min of water from an initial pressure of 82470 Pa to a final pressure of 275,800 Pa. The diameter of the inlet pipe to the pump is 15.24 cm and the diameter of the discharge pipe is 10.16 cm. What is the work? 27. A turbine operates under steady flow conditions receiving steam at the following state: pressure 1200 kPa, temperature 1880C, enthalpy 2785 kJ/kg, speed 33.3 m/s and elevation 3m. The steam leaves the turbine at the following state; pressure 20 kPa, enthalpy 2512 kJ/kg, speed 100 m/s and elevation 0m. Heat is lost to the surroundings at the rate of 0.29 kJ/s. If the rate of steam flow through the turbine is 0.42 kg/s, what is the power output of the turbine in kW? 28. Assuming that there are no heat effects and no frictional effects, find the kinetic energy and speed of a 3220-lb body after it falls 778 ft from rest. Start with the steady flow equation, deleting energy terms which are irrelevant. 29. A reciprocating compressor draws in 500 cubic feet per minute of air whose density is 0.079 lb/ft3 and discharges it with a density of 0.304 lb/ft3. At the suction, p1=15 psia; at discharge, p2=80 psia. The increase in the specific internal energy is 33.8 BTU/lb and the heat transferred from the air by cooling is

377.2 lb 11.72 slugs 0.025 ft3/lb 39.66 lb/ft3 1455 ft

13.28 kPa 221.24 kPa; 48 kPa 790.83 kPa 74.213 kPa 358.591 kPa

15000 lb/hr 10.42 fps

621.2 lb/min 93.97 min

13.24 BTU/lb 3.12 Hp

251 BTU/lb 1014 lb/hr

-2954 kJ/min

-458.1 kJ/min

112.52 kW

224 fps 56.25 Hp

30. 31.

32.

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13 BTU/lb. Determine the work on the air in BTU/min and in Hp. Neglect change in kinetic energy. Steam enters a turbine with an enthalpy of 1292 BTU/lb and leaves with an enthalpy of 1098 BTU/lb. The transferred heat is 13 BTU/lb. What is the work in BTU/min and in Hp for a flow of 2 lb/s? A thermodynamic steady flow system receives 4.56 kg per min of a fluid where p1=137.90 kPa, v1=0.0388 m3/kg, v1=122 m/s, u1=17.16 kJ/kg. The fluid leaves the system at a boundary where p2=551.6 kPa, v2=0.193 m3/kg, v2=183 m/s and u2=52.80 kJ/kg. During passage through the system the fluid receives 3000 J/s of heat. Determine the work. Air flows steadily at the rate of 0.5 kg/s through an air compressor, entering at 7 m/s speed, 100 kPa pressure nd, 0.95 m3/kg specific volume, and leaving at 5 m/s, 700 kPa, and 0.19 m3/kg. The internal energy of the air is 90 kJ/kg greater than that of the air entering. Cooling water in the compressor jackets absorbs heat from the air at the rate of 58 kW. Compute the work in kW. In a steady flow apparatus, 135 kJ of work is done by each kg of fluid. The specific volume of the fluid, pressure, and speed at the inlet are 0.37 m3/kg, 600 kPa, and 16 m/s. The inlet is 32 m above the floor, and the discharge pipe is at floor level. The discharge conditions are 0.62 m3/kg, 100 kPa, and 270 m/s. The total heat loss between the inlet and the discharge is 9 kJ/kg of fluid. In flowing through this apparatus, does the specific internal energy increase or decrease, and by how much? Steam enters a turbine stage with an enthalpy of 3628 kJ/kg at 70 m/s and leaves the same stage with an enthalpy of 2846 kJ/kg and a velocity of 124 m/s. Calculate the work done by the system. A drum 6 inches in diameter and 40 inches long contained acetylene at 250 psia and 900F. After some of the acetylene was used, the pressure was 200 psia and the temperature was 850F, a. What proportion of the acetylene was used? b. What volume would the used acetylene occupy at 14.7 psia and 80 0F? R for acetylene is 59.35 ft-lb/lb-0R The volume of a 6x12 ft tank is 339.3 cubic feet. It contains air at 200 psig and 850F. How many 1 cubic feet drums can be filled to 50 psig and 80 0F if it is assumed that the air temperature in the tank remains at 85 0F? The drums have been sitting around in the atmosphere which is at 14.7 psia and 80 0F. It is planned to lift and move logs from almost inaccessible forest areas by means of balloons. Helium at atmospheric pressure (101.325 kPa) and temperature 21.10C is to be used in the balloons. What minimum balloon diameter (assume spherical shape) will be required for a gross lifting force of 20 metric tons? Two vessels A and B of different sizes are connected by a pipe with a valve. Vessel A contains 142 L of air at 2767.92 kPa, 93.33 0C. Vessel B, of unknown volume, contains air at 68.95 kPa, 4.440C. The valve is opened and, when the properties have been determined, it is found that pm=1378.96 kPa, tm=43.330C. What is the volume of vessel B? For a certain ideal gas R=25.8 ft-lb/lb-0R and k=1.09 a. What are the values of cp and cv? b. What mass of this gas would occupy a volume of 15 ft3 at 75 psia and 80 0F? c. If 30 BTU are transferred to this gas at constant volume in (b), what are the resulting temperature and pressure? For a certain gas R=320 J/kg-K and cv=0.84 kJ/kg-K. a. Find cp and k b. If 5 kg of this gas undergo a reversible non-flow constant pressure process from V1=1.133 m3 and p1=690 kPa to a state where t2=5550C, find ΔU and ΔH. An automobile tire is inflated to 32 psig pressure at 50 0F. After being driven the temperature rise to 750F. Determine the final gage pressure assuming the volume remains constant. If 100 ft3 of atmospheric air at zero Fahrenheit temperature are compressed to a volume of 1 ft3 at a temperature of 2000F, what will be the pressure of the air in psi?

512.3 Hp

-486 kJ/min

-122 kW

-20.01 kJ/kg

776.8 kJ/kg

19.26% 2.105 ft3

1009

33.3m

110.4 L cp=312.47 ft-lb/lb-0R;0.4016 BTU/lb-0R cv=0.3685 BTU/lb-0R m=11.63 lb p2=76 psia 1.16 kJ/kg-K k-1.381 ΔU=1425.5 kJ ΔH=1968.5 kJ 34.29 psig 2109 psig

43. A 10 ft3 tank contains gas at a pressure of 500 psia, temperature of 85 0F and a weight of 25 pounds. A part of the gas was discharged and the temperature and pressure changed to 700F and 300 psia, respectively. Heat was supplied and the temperature was back to 850F. Find the final weight, volume and pressure of the gas. 44. Four hundred cubic centimeters of a gas at 740 mm Hg absolute and 18 0C undergoes a process until the pressure becomes 760 mm Hg absolute and the temperature 00C. What is the final volume of the gas? 45. A motorist equips his automobile tires with a relief-type valve so that a pressure inside the tire never will exceed 240 kPa (gage). He starts a trip with a pressure of 200 kPa (gage) and a temperature of 230C in the tires. During the long drive, the temperature of the air in the tires reaches 83 0C. Each tire contains 0.11 kg of air. Determine a. The mass of air escaping each tire, b. The pressure of the tire when the temperature returns to 23 0C. 46. A 6-m3 tank contains helium at 400K and is evacuated from atmospheric pressure to a pressure of 740 mm Hg vacuum. Determine a. Mass of helium remaining in the tank b. Mass of helium pumped out c. The temperature of the remaining helium falls to 10 0C. What is the pressure in kPa? 47. An automobile tire contains 3730 cubic inches of air at 32 psig and 80 0F a. What mass of air is in the tire? b. In operation, the air temperature increases to 145 0F. If the tire is inflexible, what is the resulting percentage increase in gage pressure? c. What mass of the 1450F air must be bled off to reduce the pressure back to its original value? 48. A spherical balloon is 40 ft in diameter and surrounded by air at 60 0F and 29.92 in Hg abs. a. If the balloon is filled with hydrogen at a temperature of 70 0F and atmospheric pressure, what total load can it lift? b. If it contains helium instead of hydrogen, other conditions remaining the same, what load can it lift? 49. A reservoir contains 2.83 m3 of carbon monoxide at 6895 kPa and 23.6 0C. An evacuated tank is filled from the reservoir to a pressure of 3497 kPa and a temperature of 12.40C, while the pressure in the reservoir decreases to 6205 kPa and the temperature to 18.30C. What is the volume of the tank? R for Co is 296.92 J/kg-K 50. A gas initially at 15 psia and 2 ft3 undergoes a process to 90 psia and 0.60 ft3, during which the enthalpy increases by 15.5 BTU; cv=2.44 BTU/lb-0R. Determine: a. ΔU b. cp c. R 51. For a certain gas, R=0.277 kJ/kg-K and k=1.384. a. What are the value of cp and cv? b. What mass of this gas would occupy a volume of 0.425 m 3 at 517.11 kPa and 26.70C c. If 31.65 kJ are transferred to this gas at constant volume in (b), what are the resulting temperature and pressure? 52. Ten cubic feet of air at 300 psia and 4000F is cooled to 1400F at constant volume. What are a. Final temperature b. The work c. The change in internal energy d. The transferred heat e. The change of enthalpy f. The change of entropy 53. There are 1.36 kg of gas, for which R=377 J/kg-K and k=1.25, that undergo a non-flow constant volume process from p1=551.6 kPa and t1=600C to p2=1655 kPa. During the process the gas is internally stirred and there are also added 105.5 kJ of heat. Determine

15.43 lb 10 ft3 308.5 psia 365 cc

0.0064 kg 182.48 kPa

0.01925 kg 0.7123 kg 1.886 kPa

0.5041 lb 17.53% 0.0542 lb

2381 lb 2209 lb

0.451 m3

11.06 BTU 3.42 BTU/lb-0R 762.4 ft-lb/lb-0R

0.7214 and 0.004 kJ/kg-K 2.647 kg 43.270C 545.75 kPa 209 psia 0 -420 BTU -420 BTU -588 BTU -0.581 BTU/0R 999K -1260.5 kJ 2.253 kJ/K

54.

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a. T2 b. The work input c. The change in entropy A group of 50 persons attended a secret meeting in a room which is 12 meters wide by 10 meters long and a ceiling of 3 meters. The room is completely sealed off and insulated. Each person gives off 150 kcal per hour of heat and occupies a volume of 0.2 cubic meter. The room has an initial pressure of 101.3 kPa and temperature of 160C. Calculate the room temperature after 10 minutes. A 1 Hp stirring motor is applied to a tank containing 22.7 kg of water. The stirring action is applied for 1 hour and the tank loses 850 kJ/hr of heat. Calculate the rise in temperature of the tank after 1 hour, assuming that the process occurs at constant volume and that cv for water is 4.187 kJ/kg- 0C. A closed constant-volume system receives 10.5 kJ of paddle work. The system contains oxygen at 344 kPa, 278 K, and occupies 0.06 m3. Find the heat (gain or loss) if the final temperature is 400K. During an isothermal process at 880F, the pressure on 8lb of air drops from 80 psia to 5 psig. For an internally reversible process, determine a. the work of a non-flow process b. the work of a steady flow process c. Q d. ΔU and ΔH e. ΔS During a reversible process there are abstracted 317 kJ/s from 1.134 kg/s of a certain gas while the temperature remains constant at 26.7 0C. for this gas, cp=2.232 and cv=1.713 kJ/kg-K. The initial pressure is 586 kPa. For both nonflow and steady flow process, determine a. V1, V2, p2 b. Work c. ΔS and ΔH Air flows steadily through an engine at constant temperature, 400K. Find the work per kilogram if the exit pressure is one-third the inlet pressure and the inlet pressure is 207 kPa. Assume that the kinetic and potential energy variation is negligible.

60. From a state defined by 300 psia, 100 ft3 and 2400F, helium undergoes and isentropic process to 0.3 psig. Find a. V2 and t2 b. ΔU and ΔH c. Ws d. Wn e. Q and ΔS 61. An adiabatic expansion of air occurs through a nozzle from 828 kPa and 71 0C to 138 kPa. The initial kinetic energy is negligible. For an isentropic expansion, compute the specific volume, temperature and speed at the exit section. 62. During a polytropic process, 10 lb of an ideal gas, whose R=40 ft-lb/lb- 0R and cp=0.25 BTU/lb-0R, changes state from 20 psia and 400F to 120 psia and 3400F. Determine: a. n b. ΔU and ΔH c. ΔS d. Q e. Non-flow work f. Steady flow-work 63. Compress 4 kg/s of CO2 gas polytropically (pV1.2=C) from p1=103.4 kPa, t1=600C to t2=2270C. Assuming ideal gas action, find p2, W, Q, ΔS as nonflow. 64. A perfect gas has a value of R=58.8 ft-lb/lb- 0R and k=1.26. if 20 BTU are added to 5 lb of this gas at constant volume when the initial temperature is 90 0F, find: a. T2 b. ΔH c. ΔS

33.10C

19.3C0

12.49 kJ 421.2 BTU 421.2 BTU 421.2 BTU 0 0 0.7686 BTU/0R 0.301 m3/s 0.0498 m3/s 3542 kPa -317 kJ/s -1.058 kJ/K-s 0 126.1 kJ 603.4 ft3 -248.70F -5822 BTU -9698 BTU 5822 BTU 9698 BTU 0 0 0.1193 m3/kg -670C 527.1 m/s n=1.356 ΔU=595.8 BTU ΔH=750 BTU ΔS=0.2543 BTU/0R Q=162.3 BTU Wn=-433.3 BTU Ws=-587.6 BTU P2=1184.9 kPa W=-631.13 kJ/s Q=-193.8 kJ/s ΔS=-0.4694 kJ/K-s T2=563.8 0R ΔH=25.27 BTU ΔS=0.036 BTU/0R ΔU=20.06 Wn=

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d. ΔU e. Work for non-flow process. A reversible, non-flow, constant volume process decreases the internal energy by 316.5 kJ for 2.268 kg of gas for which R=430 J/kg-K and k=1.35. For the process, determine a. The work b. Q c. ΔS The initial temperature is 204.4 0C. A 10 ft3 vessel of hydrogen at a pressure of 305 psia is vigorously stirred by paddles until the pressure becomes 400 psia. Determine a. ΔU b. W No heat is transferred, cv=2.434 BTU/lb-0R Three pounds of a perfect gas with R=38 ft-lb/lb-0R and k=1.667 have 300 BTU of heat added during a reversible non-flow constant pressure change of state. The initial temperature is 1000F. Determine the a. Final temperature b. ΔH c. W d. ΔU e. ΔS While the pressure remains constant at 689.5 kPa the volume of a system of air changes from 0.567 m3 to 0.283 m3. What are a. Final temperature b. ΔH c. W d. ΔU e. ΔS Four pounds of air gain 0.491 BTU/0R of entropy during a non-flow isothermal process. If p1=120 psia and V2=42.5 ft3, find: a. V1 and T1 b. W c. Q d. ΔU If 10 kg/min of air are compressed isothermally from p1=96 kPa and V1=7.65 m3/min to p2=620 kPa, find the work, the change of entropy and the heat for: A. Non-flow process B. Steady flow process with v1=15 m/s and v2=60 m/s One pound of an ideal gas undergoes an isentropic process from 95.3 psig and a volume of 0.6 ft3 to a final volume of 3.6 ft3. If cp=0.124 and cv=0.093 BTU/lb0R, what are: a. T2 b. P2 c. ΔH d. W A certain ideal gas whose R=278.6 J/kg-K and cp=1.015 kJ/kg-K expands isentropically from 1517 kPa, 2880C to 965 kPa. For 454 g/s of this gas determine, a. Wn b. V2 c. ΔU d. ΔH A polytropic process of air from 150 psia, 3000F, and 1 ft3 occurs to p2=20 psia in accordance with pv1.3=C. Determine a. T2 and V2 b. ΔU, ΔH and ΔS c. Non-flow work d. Steady flow work The work required to compress a gas reversibly according to pV1.30=C is 67790 J, if there is no flow. Determine ΔU and Q if the gas is a. Air

0 -316.5 kJ -0.7572 kJ/K

434 BTU -434 BTU

9190F 120 BTU 180 BTU 0.3301 BTU/0R

b. Methane. For methane, k=1.321, R=518.45 J/kg-K, cv=1.6187, cp=2.1377 kJ/kg-K 75. The working substance for a Carnot cycle is 8 lb of air. The volume at the beginning of isothermal expansion is 9 cubic feet and the pressure is 300 psia. The ratio of expansion during the addition of heat is 2 and the temperature of the cold body is 900F. Find: a. QA b. QR c. V3 d. P3 e. V4 f. P4 g. Pm h. The ratio of expansion during the isentropic process i. Overall compression ratio.