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2. At a 1 GW power plant the steam enters the turbines at 500 °C and the waste heat is expelled into the environment at 20 °C. (a) What is the maximum (Carnot) efficiency of the plant? (b) Assuming an actual efficiency of 40%, at what rate is waste heat expelled? (c) Now assume that the plant uses the Rankine cycle. What is the theoretical maximum efficiency of the plant now? Use the tables on page 2 for the necessary parameters. Assume that the high pressure isobar is at 100 bar.
T P (°C) (bar) 0 0.006 10 0.012 20 0.023 30 0.042 50 0.123 100 1.013 Hwater (kJ) 0 42 84 126 209 419 Hsteam Swater Ssteam (kJ) (kJ/K) (kJ/K) 2501 0 9.156 2520 0.151 8.901 2538 0.297 8.667 2556 0.437 8.453 2592 0.704 8.076 2676 1.307 7.355 Table 4.1. Properties of saturated water/steam. Pressures are given in bars, where 1 bar = 10 Pa = 1 atm. All values are for 1 kg of fluid, and are measured relative to liquid water at the triple point (0.01°C and 0.006 bar). Excerpted from Keenan et al. (1978). 600 P (bar) 1.0 3.0 10 200 H (kJ) 2875 S (kJ/K) 7.834 H (kJ) 2866 S (KJ/K) 7.312 H (kJ) 2828 S (kJ/K) 6.694 H (kJ) S (kJ/K) H (kJ) S (kJ/K) H (kJ) S (kJ/K) Temperature (°C) 300 400 500 3074 3278 3488 8.216 8.544 8.834 3069 3275 3486 7.702 8.033 8.325 3051 3264 3479 7.123 7.465 7.762 2994 3231 3457 6.539 6.921 7.234 3097 3374 6.212 6.597 2151 3081 4.473 5.791 3705 9.098 3703 8.589 3698 8.029 3682 7.509 3625 6.903 3444 6.233 30 100 300 Table 4.2. Properties of superheated steam. All values are for 1 kg of fluid, and are measured relative to liquid water at the triple point. Excerpted from Keenan et al. (1978).