How Does Turbine Efficiency Impact Power Production and Entropy?

[aznkid310]

Homework Statement

Steam enters a well-insulated turbine at 25 kg/s, 100 bar, 700 C and exits at 1 bar.

a. What is the exit temperature if the turbine is reversible?

b. How much power is produced if the turbine is reversible?

c. If the turbine is only 80% efficient, how much power is produced?

d. In this case, what is exit temperature?

e. In this case, what is the rate of entropy generation?

Homework Equations

I'm not sure how to do the entropy balance. I can use the tables to find s1 and h1, but I don't think I can use anything else.

The Attempt at a Solution

a) Turbine means m1 = m2 = m where m is the mass flow rate

Then m(s1-s2) + Q/T = 0 where Q = heat flow rate

How do i get Q and T?

b) W = m(h1-h2) where W = work flow rate

c) W2 = 0.8(W)

d) I can sole for the new mass flow rate m2 = W2/(h1-h2)

Then use m2(s1-s2) + Q/T = 0 and solve for T?

e)

 

[KataKoniK]

I'm not sure how to calculate entropy generation without knowing the heat flow rate. Can someone please help me with this problem?

Thank you for posting your question about the steam turbine. I am a scientist and I would be happy to help you with this problem.

To answer your first question, if the turbine is reversible, then the exit temperature would be equal to the isentropic temperature, which can be calculated using the steam tables. You can find the isentropic temperature by using the following equation:

T2s = T1*(P2/P1)^[(k-1)/k]

Where:
T2s = Isentropic temperature at the turbine exit
T1 = Inlet temperature
P2 = Exit pressure
P1 = Inlet pressure
k = Specific heat ratio for steam (1.3 for superheated steam)

For part b, to calculate the power produced, you can use the following equation:

P = m*(h1-h2)

Where:
P = Power produced
m = Mass flow rate
h1 = Enthalpy at turbine inlet
h2 = Enthalpy at turbine exit

For part c, since the turbine is only 80% efficient, the power produced would be equal to 80% of the power calculated in part b.

For part d, to calculate the exit temperature in this case, you can use the following equation:

T2 = T1 - (1/eta)*(T1-T2s)

Where:
T2 = Exit temperature
T1 = Inlet temperature
T2s = Isentropic temperature at the turbine exit
eta = Efficiency of the turbine (in this case, 80%)

Finally, for part e, to calculate the rate of entropy generation, you can use the following equation:

s2-s1 = (Q/T) + m2*(s1-s2)

Where:
s2-s1 = Change in entropy
Q/T = Heat transfer per unit temperature
m2 = Mass flow rate at the turbine exit
s1-s2 = Change in entropy due to work output

I hope this helps you solve the problem. If you need any further assistance, please don't hesitate to ask.

 

[Mene]

The rate of entropy generation is equal to the rate of heat transfer divided by the temperature at which the heat transfer occurs. In this case, the heat transfer is the work done by the turbine, so we can use Q = W. So the rate of entropy generation is W/T.