GATE ME 2014 Set 1 — Question 59
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Thermodynamics → Power Cycles → Rankine, Reheat & Regenerative
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Question
An ideal reheat Rankine cycle operates between the pressure limits of 10 kPa and 8 MPa, with reheat being done at 4 MPa. The temperature of steam at the inlets of both turbines is 500°C and the enthalpy of steam is 3185 kJ/kg at the exit of the high pressure turbine and 2247 kJ/kg at the exit of low pressure turbine. The enthalpy of water at the exit from the pump is 191 kJ/kg. Use the following table for relevant data.
Disregarding the pump work, the cycle efficiency (in percentage) is _______
| Superheated steam temperature ( C) | Pressure (MPa) | () | (kJ/kg) | (kJ/kg.K) |
|---|---|---|---|---|
| 500 | 4 | 0.08644 | 3446 | 7.0922 |
| 500 | 8 | 0.04177 | 3399 | 6.7266 |
Correct answer
40 to 42
Solution
1.Identify enthalpies at all states:
- State 1 (HP turbine inlet): kJ/kg (from table at 8 MPa, 500°C)
- State 2 (HP turbine exit): kJ/kg (given)
- State 3 (LP turbine inlet after reheat): kJ/kg (from table at 4 MPa, 500°C)
- State 4 (LP turbine exit): kJ/kg (given)
- State 5 (Pump exit/Boiler inlet): kJ/kg (given)
Heat is added in the boiler and the reheater.
kJ/kg
3.Calculate total work output ():
Work is produced by the HP and LP turbines.kJ/kg
4.Calculate cycle efficiency ():
Disregarding pump work, The efficiency is approximately 40.73%, which falls within the range of 40 to 42.
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