Where is Point 1 in the Rankine and Carnot Cycle?

[ShaunG123]

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

 

[BvU]

Hi,

What does $x_1=0\$ mean according to you ?

 

[ShaunG123]

it would change h1 to 145(2564-145) = 350755 however when worked through the numbers don't come out

 

[BvU]

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 !

 

[ShaunG123]

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.

 

[ShaunG123]

x1 is the dryness fraction before compression however the system is fully saturated so this should =0

 

[Chestermiller]

The fluid leaving the boiler is vapor, not liquid.

 

[ShaunG123]

how would this change the math?

 

[Chestermiller]

It would change the dryness fraction entering the condenser, and the heat load of the condenser.

 

[ShaunG123]

could you inform me what the equation would become as I am really struggling to understand this.

 

[Chestermiller]

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 $s_{g2}=5.614\ kJ/(kg-K)$.

 

[Chestermiller]

Where is point 1 supposed to be?