Answer:
Step-by-step explanation:
1. The thermal efficiency of the Carnot cycle is always higher than that of the Otto and Stirling cycles, as it is the most efficient cycle possible between the same temperature limits. The efficiency of the Stirling cycle is typically higher than that of the Otto cycle, but both are less efficient than the Carnot cycle.
2. At high pressure ratios, the temperature of the gas leaving the turbine is already very low, and therefore the benefits of regeneration are reduced. In addition, the increased pressure drop across the regenerator can reduce the efficiency of the overall cycle. Therefore, there is some truth to the claim that regeneration can decrease the thermal efficiency of a gas-turbine engine at high pressure ratios.
3. For an ideal Stirling engine using helium as the working fluid operating between temperature limits of 300 and 2000 K and pressure limits of 150 kPa and 3 MPa with a mass of helium used in the cycle of 0.12 kg:
(a) The thermal efficiency of the cycle can be calculated as:
η = 1 - T_L / T_H = 1 - (300 K / 2000 K) = 0.85 or 85%
(b) The amount of heat transfer in the regenerator can be calculated using the equation:
Q_regen = mC_p(T_H - T_C)/2 = (0.12 kg)(5190 J/kg*K)((2000 K - 300 K)/2) = 1.5 x 10^6 J
(c) The work output per cycle can be calculated using the equation:
W = Q_H - Q_L = mC_p(T_H - T_L) - Q_regen = (0.12 kg)(5190 J/kg*K)(2000 K - 300 K) - 1.5 x 10^6 J = 5.36 x 10^5 J.