ENGINEERING THERMODYNAMICS CARNOT CYCLE 1. A Carnot engine operates with 0.136 kg of air as the working substance. The pressure and volume at the beginning of isothermal expansion are 2.1 MPa and 9.6 liters. The air behaves as an ideal gas, the sink temperature is 50°C, and the heat added is 32 kJ. Determine (a) the source temperature; (b) the cycle efficiency; (c) the pressure at the end of isothermal expansion; and (d) the heat rejected to the sink per cycle. 2. A Camot engine rejects 1000 Btu/min at 500F and produces 40 hp. Determine (a) the temperature of heat addition and (b) the amount of heat flow into the engine. 3. A Camot engine produces 25 kW while operating between temperature limits of 1000 K and 300 K. Determine (a) the heat supplied per second; and (b) the heat rejection per second. 4. A Carnot engine using 1lbm air has the following conditions: heat addition beginning at 2200 psia and 22000R and continuing until the pressure is 1400 psia; isothermal compression from 14.7 psia and 5400R and continuing until the pressure is 23.1 psia. Determine (a) the heat transfer into the cycle; (b) the heat transfer from the cycle; (c) the work for each of the processes; and (d) the cycle efficiency.
8. A Carnot engine uses air as the working substance. There is 10 Btu/lbm of heat added, the pressure at the beginning of adiabatic expansion is 200 psia, and the specific volume is 1.3 ft3/lbm. The sink temperature is 400F. Determine the engine efficiency and the net work per unit mass. 9. A Camot cycle uses nitrogen as the working substance. The heat supplied is 54 kJ. The temperature of the heat rejected is 21 0C, and V3/V2 = 10. Determine (a) the cycle efficiency; (b) the temperature of heat added; and (c) the net work. 10. A Camot engine uses air and operates between temperature limits of 7400F and 400F. The pressure at state 1 is 200 psia, and the specific volume doubles during the heat addition process. Determine the net work per unit mass. 11. Helium is used in a Carnot engine where the volumes beginning with the constant temperature heat addition are V1 = 0.3565 m3, V2 = 0.5130 m3, V3 = 8.0 m3, and V4 = 5.57 m3.Determine the thermal efficiency. 12. A Camot cycle uses air as the working substance. The heat supplied is 50 Btu. The temperature of the heat rejected is 700F, and V4/V1 = 10. Determine (a) the cycle efficiency; (b) the temperature of heat added; and (c) the net work.
5. A Carnot engine uses nitrogen as the working fluid. The heat supplied is 53 kJ, and the adiabatic expansion ratio is 16: 1. The receiver temperature is 295 K. Determine (a) the thermal efficiency; (b) the heat rejected; and (c) the net work.
13. Air is used i n a Carnot eng ine where 22 kJ of heat is received at 560 K. Heat is rejected at 270 K. The displacement volume is 0.127 m3. Determine (a) the work; and (b) the mean effective pressure.
6. A Camot engine operates between 12000F and 1000F and rejects 40 Btu to the low temperature heat reservoir. Find the net work.
14. A Camot engine uses air as the working substance, receives heat at a temperature of 6000F, and rejects it at 150 0F. The maximum possible cycle pressure is 1000 psia, and minimum volume is 0.03 ft3. When heat is added, the volume increases by a factor of 2.5. Determine the pressure and volume at each state in the cycle.
7. A Carnot engine uses a ir as the working substance, receives heat at a temperature of 3150C, and rejects it at 650C. The maximum possible cycle pressure is 6.0 MPa, and the minimum volume is 0.95 liter. When heat is added, the volume increases by 250%. Determine the pressure and volume at each state in the cycle.
Prepared by ENGR. ROBERT A. MENDOZA, ME SEPTEMBER 2014
ENGINEERING THERMODYNAMICS THREE-PROCESS CYCLE 15. Two reversible engines operate in series between a high-temperature (T H) and a low temperature (TL) reservoir. Engine A rejects heat to engine B, which in tum rejects heat to the low-temperature reservoir. The high-temperature reservoir supplies heat to engine A. Let TH = 1000 K and T L = 400 K, and the engine thermal efficiencies are equal. The heat received by engine A is 500 kJ. Determine (a) the temperature of heat rejection by engine A; (b) the works of engine A and engine B; and (c) the heat rejected by engine B. 16. A Carnot engine receives 1000 Btu of heat from a heat reservoir at an unknown temperature and rejects 400 Btu of heat to a low-temperature reservoir at 770F. Determine (a) the high temperature; and (b) the thermal efficiency. 17. A Camot engine receives 1000 kJ of heat from a heat reservoir at an unknown temperature and rejects 400 kJ of heat to a low-temperature reservoir at 25 0C. Determine (a) the high temperature; and (b) the thermal efficiency. 18. A Carnot engine operating between temperature limits of 10000F and 5000F produces 80,000 ft-lbf of work. Calculate (a) the heat rejected, in BTU, and (b) the thermal efficiency of the engine. 19. Gaseous nitrogen actuates a Carnot power cycle in which the respective volumes at the four corners of the cycle starting at the beginning of the isothermal expansion are, V1 = 10.10 li, V2 = 14.53 li, V3 = 226.54 li, and V4 = 157.73 li. The cycle receives 21.5 kJ of heat. Determine (a) the net work, (b) the mean effective pressure, and (c) the thermal efficiency of the cycle. 20. A heat engine is operating on a Carnot cycle and has a thermal efficiency of 55 percent. The waste heat from this engine is rejected to a nearby lake at 60°F at a rate of 800 Btu/min. Determine (a) the power output of the engine and (b) the temperature of the source.
1. A three-process cycle operating with nitrogen as the working substance has constant temperature compression 1-2 (t 1 = 40°C, p 1 = 110 kPa); constant volume heating 2-3; and polytropic expansion 3-1 (n = 1.35). The isothermal compression requires -67 kJ/kg of work. Determine (a) p, T, and v around the cycle; (b) the heats in and out; (c) the net work. 2.
Two kg of helium operates on a three-process cycle where the processes are constant volume (1-2); constant pressure (2-3); and constant temperature (3-1). Given that p1 = 100 kPa, T 1 = 300 K, and ν1 /ν3 = 5, determine (a) the pressure, specific volume, and temperature around the cycle; (b) the work for each process; (c) the heat added.
3. Air occupies a 0.3 m3 piston-cylinder at 150 kPa and 278 K. The piston-cylinder operates on a three-process cycle where from state 1 to state 2 the pressure is constant and V2 = 1.4 V1. From state 2 to 3 the compression is reversible adiabatic until V3 = V1, and the temperature at state 3 is 450 K. A constant-volume process completes the cycle. Sketch the cycle on a p-V diagram and determine the network and heat flows for the cycle. 4. A cycle, composed of three processes, is polytropic compression (n=1.5) from 137 kPa and 380C to state 2, isobaric process from state 2 to state 3, and isometric process from state 3 going back to state 1. The heat rejected is 1560 kJ/kg and the working substance is air. Determine (a) the pressure, temperature and specific volume at states 2 and 3, (b) the heat added into the cycle and (c) the cycle net work. 5.
Two and one-half pounds of air actuates a cycle composed of the following processes: polytropic compression 1-2 with n = 1.5; constant pressure process 2-3; and constant volume process 3-1. The known data are as follows: p 1 = 20 psia, t 1 = 1000F, QR = -1682 BTU. Determine (a) the temperature and pressure at each state, (b) the net work of the cycle, and (c) the thermal efficiency.
Prepared by ENGR. ROBERT A. MENDOZA, ME SEPTEMBER 2014
