How Is Actual Power Calculated in a Turbine with Given Isentropic Efficiency?

In summary, the problem involved steam at a pressure of 4 MPa and 400 C and a flow rate of 10 kg/s being expanded in a turbine to a pressure of 10 kPa. The isentropic efficiency of the turbine was given as 0.85. The goal was to find the actual power produced by the turbine. To solve this, the formula for isentropic efficiency, ηt = (m(h1-h2))/(m(h1-h2s)) = (W act) / (W max), was used. Since s2s = s1, the value of s1 was used to find the quality at state two, which was then used to find h2. After plugging in
  • #1
dzj633

Homework Statement


Steam at a pressure of 4 MPa and 400 C and flow rate of 10 kg/s is expanded in a turbine to a pressure of 10 kPa. If the isentropic efficiency of the turbine is 0.85 then the actual power produced by the turbine is?

Homework Equations

:[/B]
ηt= (m(h1-h2))/(m(h1-h2s)) = (W act) / (W max)
s2s=s1
s2s=sf +x(sfg) <~~ To get quality
h2=hf +x(hfg)

The Attempt at a Solution


I started by looking up enthalpies and entropies at state one and two. Since s2s = s1, i used sf and sfg of P2 to find the quality and used that quality to find h2. I substituted all known values into the isentropic efficiency equation and i found h2s. After that, i plugged in all known values back into the Isentropic Eff eqn to solve for Wact and its incorrect. Did i miss a step or did them incorrectly?
 
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  • #2
dzj633 said:

Homework Statement


Steam at a pressure of 4 MPa and 400 C and flow rate of 10 kg/s is expanded in a turbine to a pressure of 10 kPa. If the isentropic efficiency of the turbine is 0.85 then the actual power produced by the turbine is?

Homework Equations

:[/B]
ηt= (m(h1-h2))/(m(h1-h2s)) = (W act) / (W max)
s2s=s1
s2s=sf +x(sfg) <~~ To get quality
h2=hf +x(hfg)

The Attempt at a Solution


I started by looking up enthalpies and entropies at state one and two. Since s2s = s1, i used sf and sfg of P2 to find the quality and used that quality to find h2. I substituted all known values into the isentropic efficiency equation and i found h2s. After that, i plugged in all known values back into the Isentropic Eff eqn to solve for Wact and its incorrect. Did i miss a step or did them incorrectly?
Please show the details of your calculations so I can check your numbers.
 
  • #3
Chestermiller said:
Please show the details of your calculations so I can check your numbers.

I figured out what I did wrong, I used: h2=h1-nt(h1-h2s) to solve for h2 and my number was correct.
 

Related to How Is Actual Power Calculated in a Turbine with Given Isentropic Efficiency?

1. What is steam and how is it related to thermodynamics?

Steam is the gaseous form of water and is related to thermodynamics because it is used as a working fluid in many thermodynamic processes, such as power generation and refrigeration.

2. How does steam produce work in a thermodynamic system?

Steam produces work by expanding and pushing against a piston, which in turn drives a turbine. This mechanical energy can then be converted into electricity or other forms of work.

3. What is the significance of the steam tables in thermodynamics?

The steam tables contain data on the thermodynamic properties of water and steam at different pressures and temperatures. This data is essential in calculating the efficiency and performance of steam-based systems.

4. How does the enthalpy of steam change during a thermodynamic process?

The enthalpy of steam changes based on the energy added or removed from the system. During a heating process, the enthalpy increases, while during a cooling process, the enthalpy decreases.

5. How does the pressure and temperature of steam affect its properties in a thermodynamic system?

The pressure and temperature of steam are directly related to its properties, such as specific volume, enthalpy, and entropy. As these variables change, the properties of steam also change, impacting the performance of the system.

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