Question

Consider a Rankine cycle operating between 1.013 bar and 100 bar with a maximum superheated steam temperature of 500ºC.

(a) Explain why H₂-H₁ is approximated as zero?

(b) Explain why (PV) points within the dashed lines have a set temperature that is determined by pressure.

(c) How much steam has condensed in the adiabatic cooling step? Give you answer as a fractional mass.

(d) How much heat per kg is removed by the condenser in 4→1?

(e) How much heat per kg is added by the boiler in 2→1?

(f) What is the efficiency of this Rankine cycle ?

Hot reservoir (Water) Boiler (Steam) Boiler \ Turbine Pump Condenser (Water + steam) Condenser Volume Cold reservoir Figure 4.8. Schematic diagram of a steam engine and the associated PV cycle (not to scale), called the Rankine cycle. The dashed lines show where the fluid is liquid water, where it is steam, and where it is part water and part steam water HsteamS water stcam (°C) (bar) (kJ)(kJ) (kJ/K) (kJ/K) 0 9.156 4225200.151 8.901 8425380.297 8.667 126 25560.4378.453 20925920.7048.076 4192676 1.307 7.355 0 0.006 10 0.012 20 0.023 30 0.042 50 0.123 100 1.013 0 2501 Table 4.1. Properties of saturated water/steam. Pressures are given in bars, where 1 bar - 105 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). Tempcraturc (°C) 200 300 400500 P (bar) 600 1.0H (kJ) 2875 3074 3278 3488 3705 S (kJ/K) 7.834 8.216 8.544 8.834 9.098 3.0H (kJ)2866 3069 3275 3486 3703 S (kJ/K) 7.312 7.702 8.033 8.325 8.589 10H (kJ) 2828 3051 3264 3479 3698 S (kJ/K) 6.694 7.123 7.465 7.762 8.029 299432313457 3682 6.539 6.921 7.234 7.509 3097 33743625 6.212 6.597 6.903 21513081 3444 4.4735.7916.233 30H (kJ) S (kJ/K) 100 H (kJ) S (kJ/K) 300H (kJ) S (kJ/K) 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).

Answer 1

Wot reseV ooile 2. 3 ,Putuq ProesJ-L ls iseㅘvo pleanr.ressim to woe pro duie. ressuAX .

Step {和。 3 sicann f.01占 2-676 du41 Le 27.41%, of Steam ,sdry rs Condensed -1-o-37462 0.12s mass Coudensed

33y Heat Remov d o coudesor to boile adld 973.9 o-313 2955 33-ig %