Chapter 9

A four-stroke turbocharged \(V-16\) diesel engine built by GE Transportation Systems to power fast trains produces 4400 hp at 1500 rpm. Determine the amount of work produced per cylinder per ( \(a\) ) mechanical cycle and ( \(b\) ) thermodynamic cycle.

Consider a simple ideal Brayton cycle operating between the temperature limits of 300 and 1500 K. Using constant specific heats at room temperature, determine the pressure ratio for which the compressor and the turbine exit temperatures of air are equal.

A four-cylinder, four-stroke spark-ignition engine operates on the ideal Otto cycle with a compression ratio of 11 and a total displacement volume of 1.8 liter. The air is at \(90 \mathrm{kPa}\) and \(50^{\circ} \mathrm{C}\) at the beginning of the compression process. The heat input is \(1.5 \mathrm{kJ}\) per cycle per cylinder. Accounting for the variation of specific heats of air with temperature, determine \((a)\) the maximum temperature and pressure that occur during the cycle, \((b)\) the net work per cycle per cyclinder and the thermal efficiency of the cycle, \((c)\) the mean effective pressure, and \((d)\) the power output for an engine speed of \(3000 \mathrm{rpm}\)

A four-cylinder spark-ignition engine has a compression ratio of \(10.5,\) and each cylinder has a maximum volume of 0.4 L. At the beginning of the compression process, the air is at \(98 \mathrm{kPa}\) and \(37^{\circ} \mathrm{C}\), and the maximum temperature in the cycle is 2100 K. Assuming the engine to operate on the ideal Otto cycle, determine \((a)\) the amount of heat supplied per cylinder, ( \(b\) ) the thermal efficiency, and \((c)\) the number of revolutions per minute required for a net power output of \(45 \mathrm{kW}\). Assume variable specific heats for air

An ideal dual cycle has a compression ratio of 14 and uses air as the working fluid. At the beginning of the compression process, air is at 14.7 psia and \(120^{\circ} \mathrm{F}\), and occupies a volume of 98 in \(^{3}\). During the heat-addition process, 0.6 Btu of heat is transferred to air at constant volume and 1.1 Btu at constant pressure. Using constant specific heats evaluated at room temperature, determine the thermal efficiency of the cycle.

Consider an ideal Stirling cycle using air as the working fluid. Air is at \(400 \mathrm{K}\) and \(200 \mathrm{kPa}\) at the beginning of the isothermal compression process, and heat is supplied to air from a source at \(1800 \mathrm{K}\) in the amount of \(750 \mathrm{kJ} / \mathrm{kg}\). Determine (a) the maximum pressure in the cycle and ( \(b\) ) the net work output per unit mass of air.

Consider a simple ideal Brayton cycle with air as the working fluid. The pressure ratio of the cycle is \(6,\) and the minimum and maximum temperatures are 300 and \(1300 \mathrm{K}\) respectively. Now the pressure ratio is doubled without changing the minimum and maximum temperatures in the cycle. Determine the change in \((a)\) the net work output per unit mass and ( \(b\) ) the thermal efficiency of the cycle as a result of this modification. Assume variable specific heats for air.

Helium is used as the working fluid in a Brayton cycle with regeneration. The pressure ratio of the cycle is 8 the compressor inlet temperature is \(300 \mathrm{K},\) and the turbine inlet temperature is \(1800 \mathrm{K}\). The effectiveness of the regenerator is 75 percent. Determine the thermal efficiency and the required mass flow rate of helium for a net power output of \(60 \mathrm{MW},\) assuming both the compressor and the turbine have an isentropic efficiency of \((a) 100\) percent and \((b) 80\) percent.

Consider an ideal gas-turbine cycle with one stage of compression and two stages of expansion and regeneration. The pressure ratio across each turbine stage is the same. The highpressure turbine exhaust gas enters the regenerator and then enters the low-pressure turbine for expansion to the compressor inlet pressure. Determine the thermal efficiency of this cycle as a function of the compressor pressure ratio and the high-pressure turbine to compressor inlet temperature ratio. Compare your result with the efficiency of the standard regenerative cycle.

A gas-turbine plant operates on the regenerative Brayton cycle with two stages of reheating and two-stages of intercooling between the pressure limits of 100 and 1200 kPa. The working fluid is air. The air enters the first and the second stages of the compressor at \(300 \mathrm{K}\) and \(350 \mathrm{K},\) respectively, and the first and the second stages of the turbine at \(1400 \mathrm{K}\) and \(1300 \mathrm{K},\) respectively. Assuming both the compressor and the turbine have an isentropic efficiency of 80 percent and the regenerator has an effectiveness of 75 percent and using variable specific heats, determine ( \(a\) ) the back work ratio and the net work output, \((b)\) the thermal efficiency, and \((c)\) the secondlaw efficiency of the cycle. Also determine ( \(d\) ) the exergies at the exits of the combustion chamber (state 6 ) and the regenerator (state 10 ) (See Fig. \(9-43\) in the text).