Problem 60
The compression ratio of an ideal dual cycle is 14. Air is at \(100 \mathrm{kPa}\) and \(300 \mathrm{K}\) at the beginning of the compression process and at \(2200 \mathrm{K}\) at the end of the heat-addition process. Heat transfer to air takes place partly at constant volume and partly at constant pressure, and it amounts to \(1520.4 \mathrm{kJ} / \mathrm{kg} .\) Assuming variable specific heats for air, determine \((a)\) the fraction of heat transferred at constant volume and \((b)\) the thermal efficiency of the cycle.
Problem 64
An air-standard cycle, called the dual cycle, with constant specific heats is executed in a closed piston-cylinder system and is composed of the following five processes: \(1-2 \quad\) Isentropic compression with a compression ratio \(r=V_{1} / V_{2}\) \(2-3 \quad\) Constant volume heat addition with a pressure ratio, \\[ r_{p}=P_{3} / P_{2} \\] \(3-4 \quad\) Constant pressure heat addition with a volume ratio \\[ r_{c}=V_{4} / V_{3} \\] \(4-5 \quad\) Isentropic expansion while work is done until \(V_{5}=V_{1}\) \(5-1 \quad\) Constant volume heat rejection to the initial state (a) Sketch the \(P\) -V and \(T\) -s diagrams for this cycle. (b) Obtain an expression for the cycle thermal efficiency as a function of \(k, r, r_{c},\) and \(r_{p}\) (c) Evaluate the limit of the efficiency as \(r_{p}\) approaches unity and compare your answer with the expression for the Diesel cycle efficiency. (d) Evaluate the limit of the efficiency as \(r_{c}\) approaches unity and compare your answer with the expression for the Otto cycle efficiency.
Problem 65
What cycle is composed of two isothermal and two constant-volume processes?
Problem 66
How does the ideal Ericsson cycle differ from the Carnot cycle?
Problem 67
Consider the ideal Otto, Stirling, and Carnot cycles operating between the same temperature limits. How would you compare the thermal efficiencies of these three cycles?
Problem 68
Consider the ideal Diesel, Ericsson, and Carnot cycles operating between the same temperature limits. How would you compare the thermal efficiencies of these three cycles?
Problem 69
An ideal Ericsson engine using helium as the working fluid operates between temperature limits of 550 and \(3000 \mathrm{R}\) and pressure limits of 25 and 200 psia. Assuming a mass flow rate of \(14 \mathrm{lbm} / \mathrm{s}\), determine (a) the thermal efficiency of the cycle, \((b)\) the heat transfer rate in the regenerator, and \((c)\) the power delivered.
Problem 70
An ideal Stirling engine using helium as the working fluid operates between temperature limits of 300 and 2000 K and pressure limits of \(150 \mathrm{kPa}\) and 3 MPa. Assuming the mass of the helium used in the cycle is \(0.12 \mathrm{kg}\), determine \((a)\) the thermal efficiency of the cycle, \((b)\) the amount of heat transfer in the regenerator, and \((c)\) the work output per cycle.
Problem 71
Consider an ideal Ericsson cycle with air as the working fluid executed in a steady-flow system. Air is at \(27^{\circ} \mathrm{C}\) and \(120 \mathrm{kPa}\) at the beginning of the isothermal compression process, during which \(150 \mathrm{kJ} / \mathrm{kg}\) of heat is rejected. Heat transfer to air occurs at \(1200 \mathrm{K}\). Determine \((a)\) the maximum pressure in the cycle, \((b)\) the net work output per unit mass of air, and \((c)\) the thermal efficiency of the cycle.
Problem 72
An ideal Stirling cycle filled with air uses a \(75^{\circ} \mathrm{F}\) energy reservoir as a sink. The engine is designed so that the maximum air volume is \(0.5 \mathrm{ft}^{3},\) the minimum air volume is \(0.06 \mathrm{ft}^{3},\) and the minimum pressure is 15 psia. It is to be operated such that the engine produces 2 Btu of net work when 5 Btu of heat are transferred externally to the engine. Determine the temperature of the energy source, the amount of air contained in the engine, and the maximum air pressure during the cycle.
