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Reheat cycle: 4 MPa, 400°C

Short answer

Using ideal reheat cycle with isentropic expansion and pump work, net work is 1293.4 kJ/kg and heat added is 3606.1 kJ/kg. Cycle efficiency is approximately 35.9%.

On a reheat cycle, steam leaves the boiler and enters the turbine at 4 MPa, 400°C. After expansion in the turbine to 400 kPa, the steam is reheated to 400°C and then expanded in the low-pressure turbine to 10 kPa. Determine the cycle efficiency. [Refer the attached table for the properties of steam].

Assumptions: ideal reheat Rankine cycle; isentropic turbines and pump; pump work included. Values from steam tables (IAPWS-IF97).

States: 1 = 4 MPa, 400 C; 2 = 400 kPa (HP exit); 3 = 400 kPa, 400 C; 4 = 10 kPa; 5 = saturated water at 10 kPa; 6 = pump exit.

               1
  +----------+----->+------+     +------+
  |  Boiler  |      |  HP  |=====|  LP  |===> Generator
  |  + S/H   |  2   | turb |     | turb |
  | Reheater |<-----+------+  +->+------+
  |          |------------3---+     | 4
  +----------+                      v
       ^ 6                    +-----------+
       |      +------+   5    | Condenser |
       +------| Pump |<-------+-----------+
              +------+

Steam table data

StateData
4 MPa, 400 Ch1=3214.4h_1 = 3214.4, s1=6.7712s_1 = 6.7712
400 kPa sat.hf=604.72h_f = 604.72, hfg=2133.33h_{fg} = 2133.33, sf=1.7766s_f = 1.7766, sfg=5.1188s_{fg} = 5.1188
400 kPa, 400 Ch3=3273.9h_3 = 3273.9, s3=7.9001s_3 = 7.9001
10 kPa sat.hf=191.81h_f = 191.81, hfg=2392.07h_{fg} = 2392.07, sf=0.6492s_f = 0.6492, sfg=7.4997s_{fg} = 7.4997, vf=0.001010v_f = 0.001010

State 2 (s2=s1s_2 = s_1)

x2=6.7712−1.77665.1188=0.9757h2=604.72+0.9757×2133.33=2686.3 kJ/kg\begin{aligned} x_2 &= \frac{6.7712 - 1.7766}{5.1188} = 0.9757 \\ h_2 &= 604.72 + 0.9757 \times 2133.33 = 2686.3\ \text{kJ/kg} \end{aligned}

State 4 (s4=s3s_4 = s_3)

x4=7.9001−0.64927.4997=0.9668h4=191.81+0.9668×2392.07=2504.5 kJ/kg\begin{aligned} x_4 &= \frac{7.9001 - 0.6492}{7.4997} = 0.9668 \\ h_4 &= 191.81 + 0.9668 \times 2392.07 = 2504.5\ \text{kJ/kg} \end{aligned}

Pump

Wp=vf(p6−p5)=0.001010(4000−10)=4.03 kJ/kgh6=191.81+4.03=195.84 kJ/kg\begin{aligned} W_p &= v_f (p_6 - p_5) = 0.001010 (4000 - 10) = 4.03\ \text{kJ/kg} \\ h_6 &= 191.81 + 4.03 = 195.84\ \text{kJ/kg} \end{aligned}

Work, heat and efficiency

WT=(h1−h2)+(h3−h4)=(3214.4−2686.3)+(3273.9−2504.5)=528.1+769.3=1297.4 kJ/kgWnet=1297.4−4.03=1293.4 kJ/kgQs=(h1−h6)+(h3−h2)=(3214.4−195.84)+(3273.9−2686.3)=3018.5+587.6=3606.1 kJ/kgη=1293.43606.1=0.3587\begin{aligned} W_T &= (h_1 - h_2) + (h_3 - h_4) \\ &= (3214.4 - 2686.3) + (3273.9 - 2504.5) \\ &= 528.1 + 769.3 = 1297.4\ \text{kJ/kg} \\ W_{net} &= 1297.4 - 4.03 = 1293.4\ \text{kJ/kg} \\ Q_s &= (h_1 - h_6) + (h_3 - h_2) \\ &= (3214.4 - 195.84) + (3273.9 - 2686.3) \\ &= 3018.5 + 587.6 = 3606.1\ \text{kJ/kg} \\ \eta &= \frac{1293.4}{3606.1} = 0.3587 \end{aligned}

Answer: cycle efficiency ≈35.9%\approx 35.9\% (net work 1293.4 kJ/kg, exhaust dryness 0.967).

  T
  ^                  1          3
  |                 /|         /|
  |                / |        / |
  |     f--------g'  |       /  |
  |    /             2------'   |
  |   /                         |
  |  6                          |
  |  5--------------------------4
  +--------------------------------> s
  5-6 pump, 6-f-g'-1 boiler (heat,
  boil, superheat), 1-2 HP turbine,
  2-3 reheater, 3-4 LP turbine,
  4-5 condenser

Compared with a simple Rankine cycle between 4 MPa, 400 C and 10 kPa (about 35.3%, exhaust dryness 0.816), reheat increases efficiency slightly, raises the net work by about 21% and makes the exhaust steam much drier.

✓ Answer checked by Claude Opus 5.5 (high effort)

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