Problem 74
An air-standard Stirling cycle operates with a maximum pressure of \(3600 \mathrm{kPa}\) and a minimum pressure of \(50 \mathrm{kPa}\) The maximum volume is 12 times the minimum volume, and the low-temperature reservoir is at \(20^{\circ} \mathrm{C}\). Allowing a \(5^{\circ} \mathrm{C}\) temperature difference between the external reservoirs and the air when appropriate, calculate the specific heat added to the cycle and its net specific work.
Problem 76
For fixed maximum and minimum temperatures, what is the effect of the pressure ratio on \((a)\) the thermal efficiency and ( \(b\) ) the net work output of a simple ideal Brayton cycle?
Problem 78
Why are the back work ratios relatively high in gasturbine engines?
Problem 79
How do the inefficiencies of the turbine and the compressor affect \((a)\) the back work ratio and \((b)\) the thermal efficiency of a gas-turbine engine?
Problem 80
A simple ideal Brayton cycle with air as the working fluid has a pressure ratio of \(10 .\) The air enters the compressor at \(520 \mathrm{R}\) and the turbine at \(2000 \mathrm{R}\). Accounting for the variation of specific heats with temperature, determine ( \(a\) ) the air temperature at the compressor exit, ( \(b\) ) the back work ratio, and \((c)\) the thermal efficiency.
Problem 81
A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers \(32 \mathrm{MW}\) of power. The minimum and maximum temperatures in the cycle are 310 and \(900 \mathrm{K},\) and the pressure of air at the compressorexit is 8 times the value at the compressor inlet. Assuming an isentropic efficiency of 80 percent for the compressor and 86 percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heats with temperature.
Problem 86
Consider a simple Brayton cycle using air as the working fluid; has a pressure ratio of \(12 ;\) has a maximum cycle temperature of \(600^{\circ} \mathrm{C} ;\) and operates the compressor inlet at \(100 \mathrm{kPa}\) and \(15^{\circ} \mathrm{C} .\) Which will have the greatest impact on the back-work ratio: a compressor isentropic efficiency of 80 percent or a turbine isentropic efficiency of 80 percent? Use constant specific heats at room temperature.
Problem 87
Air is used as the working fluid in a simple ideal Brayton cycle that has a pressure ratio of \(12,\) a compressor inlet temperature of \(300 \mathrm{K},\) and a turbine inlet temperatureof \(1000 \mathrm{K} .\) Determine the required mass flow rate of air for a net power output of \(70 \mathrm{MW}\), assuming both the compressor and the turbine have an isentropic efficiency of \((a) 100\) percent and \((b) 85\) percent. Assume constant specific heats at room temperature.
Problem 88
An aircraft engine operates on a simple ideal Brayton cycle with a pressure ratio of \(10 .\) Heat is added to the cycle at a rate of \(500 \mathrm{kW} ;\) air passes through the engine at a rate of \(1 \mathrm{kg} / \mathrm{s} ;\) and the air at the beginning of the compression is at \(70 \mathrm{kPa}\) and \(0^{\circ} \mathrm{C}\). Determine the power produced by this engine and its thermal efficiency. Use constant specific heats at room temperature.
Problem 90
A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1600 kPa. The working fluid is air, which enters the compressor at \(40^{\circ} \mathrm{C}\) at a rate of \(850 \mathrm{m}^{3} / \mathrm{min}\) and leaves the turbine at \(650^{\circ} \mathrm{C}\). Using variable specific heats for air and assuming a compressor isentropic efficiency of 85 percent and a turbine isentropic efficiency of 88 percent, determine \((a)\) the net power output (b) the back work ratio, and \((c)\) the thermal efficiency.
