- #1

MCTachyon

- 51

- 3

## Homework Statement

Superheated steam at a pressure of 40 bar and a temperature of 500°C is supplied to the turbine of a Rankine cycle. If the condenser pressure is 0.03 bar.

Find the thermal efficiency of the cycle. (Neglect feed pump work).

I used steam tables found https://www.slideshare.net/SGhallab/steam-tables-fifth-edition-by-rogers-and-mayhew

## Homework Equations

S

_{1}= S

_{g}

S

_{g}= (1 - x

_{g})S

_{f2}+ x

_{g}S

_{g2}

h

_{2}= (1 - x

_{g})h

_{f2}+ x

_{g}h

_{g2}

Specific work (W) = h

_{1}- h

_{2}

Specific Heat (Q) = h

_{1}- h

_{f2}

Eff (η) = W / Q

## The Attempt at a Solution

From steam tables:

At 40 Bar and 500°C (Before turbines):

h

_{g}= 3445 kJ Kg

^{-1}

S

_{g}= 7.089 kJ Kg

^{-1}K

^{-1}

At 0.03 Bar (After turbines):

h

_{f2}= 101 kJ Kg

^{-1}

h

_{g2}= 2545 kJ Kg

^{-1}

h

_{fg2}= 2444 kJ Kg

^{-1}

S

_{f2}= 0.354 kJ Kg

^{-1}K

^{-1}

S

_{g2}= 8.576 kJ Kg

^{-1}K

^{-1}

S

_{fg}= 8.222 kJ Kg

^{-1}K

^{-1}

-------------------------------------------------------------------------------------------------------------------------

Attempt at working out the thermal efficiency of the cycle:

S

_{g}= (1 - x

_{g})S

_{f2}+ x

_{g}S

_{g2}

7.089 = (1 - x

_{g}) * 0.354 + x

_{g}8.576

∴

x

_{g}= (7.089 - 0.345) / (8.576 - 0.345)

x

_{g}= 0.819

Now

h

_{2}= (1 - x

_{g})h

_{f2}+ x

_{g}h

_{g2}

h

_{2}= (1 - 0.819) * 101 + 0.819 * 2545

h

_{2}= 2103 kJ kg

^{-1}

∴

Specific work (W) = h

_{1}- h

_{2}

W = 3445 - 2103

W = 1342 kJ kg

^{-1}

And

Q = h

_{1}- h

_{f2}

Q = 3445 - 101

Q = 3344 kJ kg

^{-1}

∴

Eff (η) = W / Q

η = 1342 / 3344

η =

__0.4013 or 40.13% efficient__

Am I looking at the right area to solve this?