第 三 題

循環輸入熱量 $Q_{in} = C_p (T_3 - T_2) = 1.0 \times (1500 - 589.89) = 910.11 \text{ kJ/kg}$ 淨功輸出 $W_{net} = W_t - W_c = 650.77 - 299.89 = 350.88 \text{ kJ/kg}$ 熱效率 $\eta = \frac{W_{net}}{Q_{in}} \times 100% = \frac{350.88}{910.11} \times 100% \approx 38.55%$

已知：$T_1 = 17^\circ\text{C} = 290 \text{ K}$，$P_1 = 100 \text{ kPa}$，$r_p = 10$，$T_3 = 1500 \text{ K}$，$\eta_c = \eta_t = 0.9$，空氣 $k=1.4$。 狀態 1 (壓縮機進口)： $T_1 = 290 \text{ K}$， $P_1 = 100 \text{ kPa}$

根據焓差計算功： 空氣壓縮機耗功 $W_c = C_p (T_2 - T_1) = 1.0 \times (589.89 - 290) = 299.89 \text{ kJ/kg} \approx 299.9 \text{ kJ/kg}$ 渦輪機產出功 $W_t = C_p (T_3 - T_4) = 1.0 \times (1500 - 849.23) = 650.77 \text{ kJ/kg} \approx 650.8 \text{ kJ/kg}$