Question

For an ideal regenerative Rankine cycle, as shown in the figure below, which one of the following options is the correct representation of temperature-entropy (T-s) diagram?

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

Remember that an ideal pump and an ideal turbine are both isentropic, so those two legs must be vertical on the T-s diagram.

Answer 1

The Correct Option is A

The flow diagram numbers the states as 1 (condenser exit), 2 (pump exit), 3 (feedwater heated by the bled steam, entering the boiler), 4 (boiler exit, turbine inlet), and 5 (turbine exit, entering the condenser). Because the cycle is called ideal, the pump and the turbine are both taken as reversible, so both processes must run at constant entropy. On a T-s plot that means leg 1 to 2 and leg 4 to 5 must each be drawn as vertical lines, not slanted ones. The heating from 2 to 3 happens because the cold feedwater picks up heat from the extracted steam, so it must show a rise in both temperature and entropy, ending close to the saturated liquid boundary. The heating from 3 to 4 is the boiler adding the rest of the heat at essentially constant high pressure, drawn as the near horizontal top segment, and 5 to 1 is the constant pressure condensation at the bottom.

1. Option A: keeps the pump leg 1 to 2 and the turbine leg 4 to 5 vertical, with 2 to 3 rising along the compressed liquid side and 3 to 4 running across the top, matching every requirement of an ideal regenerative cycle.
2. Option B: pushes state 5 out to the far right of the dome at the same entropy as state 4 in a way that no longer matches a throttled, two phase condenser inlet, breaking the expected shape of the low pressure side of the cycle.
3. Option C: draws points 2, 3, and 4 almost on a single slanted line, which would mean the pump adds very little entropy rise relative to the boiler heating, blurring the separate feedwater heating step that regeneration is supposed to show.
4. Option D: tilts the 1 to 2 pump line noticeably to the right, implying the pump is not reversible, which contradicts the word ideal in the question.

Only option A keeps both the pump and the turbine as vertical, isentropic legs while still showing a clear separate regeneration step from 2 to 3, so option A is the correct T-s diagram.