Chapter 9 Problems

Chapter # 9 Problem solving (7th edition) Problem # 1 (9.13): an air-standard cycle is executed within a closed piston-cylinder system and consists of three processes as follows: 1-2: V = constant heat addition from 100 kPa and 27oC to 700 kPa. 2-3: isothermal expansion until V3 = 7V2. 3-1: P = constant heat rejection to the initial state. Assume air has constant properties with Cv = 0.718 kJ/kg.K, Cp = 1.005 kJ/kg.K, R = 0.287 kJ/kg.K, and k = 1.4. (a) Sketch the P-v and T-s diagrams for the cycle. (b) Determine the ratio of the compression work to the expansion work (back work ratio). (c) Determine the cycle thermal efficiency.

Problem # 2 (9.15): An air-standard cycle is executed in a closed system and is composed of the following four processes. 1-2: isentropic compression from 100 kPa and 22oC to 600 kPa. 2-3: constant volume heat addition to 1500 K. 3-4: isentropic expansion to 100 kPa. 4-1: constant pressure heat rejection to initial state. Assume air has constant properties with Cv = 0.718 kJ/kg.K, Cp = 1.005 kJ/kg.K, R = 0.287 kJ/kg.K, and k = 1.4. (a) Show the cycle on P-v and T-s diagrams. (b) Calculate the net work output per unit mass. (c) Determine the thermal efficiency.

Problem # 3 (9.30): An ideal Otto cycle has a compression ratio of 10.5, takes in air at 90 kPa and 40oC, and is repeated 2500 times per minute. Using constant specific heats at room temperature, determine the thermal efficiency of this cycle and the rate of heat input if the cycle is to produce 90 kW of power.

Problem # 4 (9.33): An ideal Otto cycle has a compression ratio of 8 and takes in air at 95 kPa and 15oC, and the maximum cycle temperature is 1200oC. Determine the heat transferred to and rejected from this cycle, as well as the cycle’s thermal efficiency. Problem # 5 (9.35): The compression ratio of an airstandard Otto cycle is 9.5. Prior to the isentropic compression process, the air is at 100 kPa, 35oC, and 600 cm3. The temperature at the end of isentropic expansion process is 800 K. Using specific heat values at room temperature, determine (a) the highest temperature and pressure in the cycle; (b) the amount of heat transferred; (c) the thermal efficiency; and (d) the mean effective pressure. Problem # 6 (9.39): A four-cylinder, four-stroke 1.6 L gasoline engine operates on the Otto cycle with compression ratio of 11. The air is at 100 kPa and 37oC at the beginning of the compression process, and the maximum pressure in the cycle is 8 MPa. The compression and expansion processes may be modelled as polytropic processes with k = 1.3. cv = 0.823 kJ/kg.K. Determine (a) the temperature at the end of the expansion process. (b) the net work output and thermal efficiency.

(c) the mean effective pressure. (d) the engine speed for a net power output of 50 kW. Problem # 7 (9.47): An ideal Diesel cycle has a compression ratio of 20 and cutoff ratio of 1.3. Determine the maximum temperature of the air and the rate of heat addition to this cycle when it produces 250 kW of power. The air is at 90 kPa and 15oC at the end of the suction stroke. Problem # 8 (9.52): An ideal Diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of the air at the beginning of the compression process is 95 kPa and 20oC. If the maximum temperature in the cycle is not to exceed 2200 K, determine (a) the thermal efficiency. (b) the mean effective pressure. Use constant specific heats at room temperature. Problem # 9 (9.57): An air-standard dual cycle has a compression ratio of 18 and cutoff ratio of 1.1. the pressure ratio during constant volume heat addition process is 1.1. At the beginning of the compression, P1 = 90 kPa, T1 = 18oC, and V1 = 0.003 m3. How much power this cycle will produce when it is executed 4000

times per minute? Use constant specific heats at room temperature.

Problem # 10 (9.59): An ideal dual cycle has a compression ratio of 15 and a cutoff ratio of 1.4. The pressure ratio during constant-volume heat addition process is 1.1. The air at the beginning of the compression is P1 = 98 kPa and T1 = 24oC. Calculate the cycle’s thermal efficiency, net specific work, and specific heat addition. Use constant specific heats at room temperature.

Problem # 11 (9.81): A simple ideal Brayton cycle with air as the working fluid has a pressure ratio of 10. The air enters the compressor at 290 K and the turbine at 1100 K. Assuming constant specific heats, determine (a) the air temperature at the compressor exit, (b) the back work ratio, and (c) the thermal efficiency.

Problem # 12 (9.85): A simple ideal Brayton cycle uses helium as the working fluid; operates with 83 kPa and 15oC at the compressor inlet; has a pressure ratio of 14; and a maximum cycle temperature of 700oC. How much power will this cycle produce when the flow rate of helium is 50 kg/min in the cycle? Use constant specific heats at room temperature. Cp = 5.1926 kJ/kg.K, k = 1.667.

Problem # 13 (9.94): A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 800 kPa. Air enters the compressor at 30oC and leaves at 330oC at a mass flow rate of 200 kg/s. The maximum cycle temperature is 1400 K. During operation of the cycle, the net power output is measured experimentally to be 60 MW. Assume constant properties of air at 300 K with cv = 0.718 kJ/kg.K, cp = 1.005 kJ/kg.K R = 0.287 kJ/kg.K, k = 1.4. (a) Sketch the T-s diagram for the cycle. (b) Determine the isentropic efficiency of the turbine for these operating conditions. (c) Determine the cycle thermal efficiency.