Problem 12
An air-standard cycle is executed within a closed piston-cylinder system and consists of three processes as follows: \(1-2 \quad V=\) constant heat addition from \(100 \mathrm{kPa}\) and \(27^{\circ} \mathrm{C}\) to \(700 \mathrm{kPa}\) \(2-3 \quad\) Isothermal expansion until \(V_{3}=7 V_{2}\) \(3-1 \quad P=\) constant heat rejection to the initial state Assume air has constant properties with \(c_{v}=0.718 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\) \(c_{p}=1.005 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}, R=0.287 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K},\) 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 (the back work ratio). (c) Determine the cycle thermal efficiency.
Problem 13
An air-standard cycle with variable specific heats is executed in a closed system and is composed of the following four processes: \(1-2 \quad\) Isentropic compression from 100 kPa and \(22^{\circ} \mathrm{C}\) to \(600 \mathrm{kPa}\) 2-3 \(\quad v=\) constant heat addition to \(1500 \mathrm{K}\) \(3-4 \quad\) Isentropic expansion to \(100 \mathrm{kPa}\) 4-1 \(P=\) constant heat rejection to initial state (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 15
An air-standard cycle is executed in a closed system with \(0.5 \mathrm{kg}\) of air and consists of the following three processes: \(1-2 \quad\) Isentropic compression from 100 kPa and \(27^{\circ} \mathrm{C}\) to \(1 \mathrm{MPa}\) \(2-3 \quad P=\) constant heat addition in the amount of \(416 \mathrm{kJ}\) \(3-1 \quad P=c_{1} v+c_{2}\) heat rejection to initial state \(c_{1}+c_{2}\) constants) (a) Show the cycle on \(P\) -v and \(T\) -s diagrams. (b) Calculate the heat rejected. (c) Determine the thermal efficiency. Assume constant specific heats at room temperature.
Problem 16
An air-standard cycle with variable specific heats is executed in a closed system and is composed of the following four processes: \(1-2 \quad v=\) constant heat addition from 14.7 psia and \(80^{\circ} \mathrm{F}\) in the amount of \(300 \mathrm{Btu} / \mathrm{lbm}\) 2-3 \(P=\) constant heat addition to \(3200 \mathrm{R}\) \(3-4 \quad\) Isentropic expansion to 14.7 psia 4-1 \(P=\) constant heat rejection to initial state (a) Show the cycle on \(P\) -V and \(T\) -s diagrams. (b) Calculate the total heat input per unit mass. (c) Determine the thermal efficiency.
Problem 18
An air-standard Carnot cycle is executed in a closed system between the temperature limits of 350 and \(1200 \mathrm{K}\) The pressures before and after the isothermal compression are 150 and \(300 \mathrm{kPa}\), respectively. If the net work output per cycle is \(0.5 \mathrm{kJ},\) determine \((a)\) the maximum pressure in the cycle, \((b)\) the heat transfer to air, and \((c)\) the mass of air. Assume variable specific heats for air.
Problem 20
Consider a Carnot cycle executed in a closed system with \(0.6 \mathrm{kg}\) of air. The temperature limits of the cycle are 300 and \(1100 \mathrm{K},\) and the minimum and maximum pressures that occur during the cycle are 20 and 3000 kPa. Assuming constant specific heats, determine the net work output per cycle.
Problem 21
Consider a Carnot cycle executed in a closed system with air as the working fluid. The maximum pressure in the cycle is 1300 kPa while the maximum temperature is \(950 \mathrm{K}\) If the entropy increase during the isothermal heat rejection process is \(0.25 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\) and the net work output is \(100 \mathrm{kJ} / \mathrm{kg}\) determine \((a)\) the minimum pressure in the cycle, \((b)\) the heat rejection from the cycle, and \((c)\) the thermal efficiency of the cycle. \((d)\) If an actual heat engine cycle operates between the same temperature limits and produces \(5200 \mathrm{kW}\) of power for an air flow rate of \(95 \mathrm{kg} / \mathrm{s}\), determine the second law efficiency of this cycle.
Problem 23
What four processes make up the ideal Otto cycle?
Problem 24
Are the processes that make up the Otto cycle analyzed as closed-system or steady-flow processes? Why?
Problem 26
How does the thermal efficiency of an ideal Otto cycle change with the compression ratio of the engine and the specific heat ratio of the working fluid?
