Where is Point 1 in the Rankine and Carnot Cycle?

  • Context: Engineering 
  • Thread starter Thread starter ShaunG123
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Discussion Overview

The discussion revolves around the Rankine and Carnot cycles, specifically focusing on the location and significance of Point 1 within these thermodynamic cycles. Participants explore the implications of changing the dryness fraction (x1) and its effect on efficiency and other parameters, including entropy and heat load.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the meaning of ##x_1=0## and its implications for the system's efficiency.
  • One participant notes that changing x1 to 0 results in drastic changes in numerical outcomes, indicating sensitivity in the calculations.
  • Another participant clarifies that x1 represents the dryness fraction before compression, suggesting it should equal 0 in a fully saturated system.
  • There is a discussion about the nature of the fluid leaving the boiler, with one participant asserting it is vapor, not liquid.
  • Participants inquire about the mathematical changes that result from altering x1 and seek clarification on the relevant equations.
  • One participant provides a detailed explanation of the entropy relationships in the system, including equations for calculating the dryness fraction based on entropy values.
  • A participant requests a schematic and list of symbols to better understand the setup, indicating a need for clearer visual aids.
  • There is a general inquiry about the location of Point 1 in the cycle, suggesting uncertainty about its definition or placement.

Areas of Agreement / Disagreement

Participants express differing views on the implications of setting x1 to 0, with some asserting it should be 0 while others highlight the resulting changes in calculations. The discussion remains unresolved regarding the exact placement and significance of Point 1.

Contextual Notes

Participants reference specific entropy values and relationships without providing complete context for their derivations, leading to potential gaps in understanding. The discussion also reflects varying assumptions about the state of the fluid at different points in the cycle.

Who May Find This Useful

This discussion may be of interest to students and professionals studying thermodynamics, particularly those focused on the Rankine and Carnot cycles and their applications in engineering contexts.

ShaunG123
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Homework Statement
By using data from the plant (given below) and thermodynamic properties tables and/or charts, you need to calculate the overall efficiencies for turbine ‘A’ which is operating on a Rankine cycle

Turbine ‘A’ uses steam as the working fluid and operates on the ideal Rankine cycle (without superheat). The boiler pressure is 10 MPa and the condenser pressure is 5.5 kPa. Assume that the operating cycle is reversible.

My attempt is below however when I change x1 to 0 the numbers don't work.
Relevant Equations
Rankine/Carnot Efficiencies
thermo (2).png
 
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Hi,

What does ##x_1=0\ ## mean according to you ?
 
it would change h1 to 145(2564-145) = 350755 however when worked through the numbers don't come out
 
Are you able to post a schematic of the setup with a list of symbols or do we have to reverse-engineer it ? I like the subject, but doing that would take some time !
 
I am just trying to figure out if i change x1 to 0 rather than the 0.364 how the efficiency would change however whenever i change this to zero the numbers change drastically.
 
x1 is the dryness fraction before compression however the system is fully saturated so this should =0
 
The fluid leaving the boiler is vapor, not liquid.
 
how would this change the math?
 
It would change the dryness fraction entering the condenser, and the heat load of the condenser.
 
  • #10
could you inform me what the equation would become as I am really struggling to understand this.
 
  • #11
Well, the entropy of the saturated vapor leaving the boiler and entering the turbine is ##s_2=s_{g2}##. Since the turbine is operating adiabatically and reversibly, this is also the entropy of the stream leaving the turbine and entering the condenser ##(s_1=s_2)##. This stream is comprised of a mixture of saturated vapor and saturated liquid at entropies ##s_{g1}## and ##s_{f1}##, respectively. In order for the overall stream to have entropy ##s_2##, the dry fraction ##x_1## of the stream must satisfy: $$s_1=s_2=xs_{g1}+(1-x)s_{f1}$$Solving for this dry fraction yields: $$x_1=\frac{s_2-s_{f1}}{s_{g1}-s_{f1}}=\frac{s_{g2}-s_{f1}}{s_{g1}-s_{f1}}$$where ##s_{g2}=5.614\ kJ/(kg-K)##.
 
Last edited:
  • #12
Where is point 1 supposed to be?
 

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