Thermodynamics - Vapour Power Plants

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SUMMARY

The discussion focuses on calculating the power input and isentropic efficiency of a compressor in a vapor power plant scenario. The compressor processes 4 kg/s of air, increasing its pressure from 1 bar to 4 bars and its temperature from 25°C to 200°C. The calculated power input is 703.5 kW, with an isentropic efficiency of 0.83. Key equations utilized include the relationship between enthalpy changes and the ideal gas properties of air.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically the First Law of Thermodynamics.
  • Familiarity with ideal gas properties and the specific heat capacities of air (Cp and Cv).
  • Knowledge of isentropic processes and efficiency calculations.
  • Ability to interpret thermodynamic tables for air, including enthalpy and relative pressure (Pr) values.
NEXT STEPS
  • Study the derivation and application of the isentropic efficiency formula in thermodynamic systems.
  • Learn how to use thermodynamic tables for various gases, focusing on enthalpy and relative pressure values.
  • Explore the impact of varying inlet conditions on compressor performance in vapor power cycles.
  • Investigate advanced thermodynamic cycles, such as the Brayton cycle, and their applications in power generation.
USEFUL FOR

Students preparing for engineering exams, thermodynamics enthusiasts, and professionals involved in the design and analysis of vapor power plants.

geordieman101
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Homework Statement


A compressor takes in 4 kg/s of air at atmospheric pressure and temperature, 1 bar and 25 degrees C. Air leaves the compressor at 4 bars and 200 degreesC. Calculate the power input to the compressor and its isentropic efficiency. For air Cp=1.005 and Cv=0.718 kJ/kg K

Answers: (703.5 kW, 0.83)

Homework Equations



(h2s - h1)/(h2-h1)

The Attempt at a Solution


I have already calculated the power input by using mass flow rate x Cp x delta T, however I am unable to find the isentropic efficiency. My attempt so far has been to divide Power input by mass flow rate to obtain h2-h1. The h2-h1 value i have obtained is 175.9kJ. I need help in finding h2s-h1.

I am doing this questions as exam preparation (this has nothing to do with coursework/homework) so maximum help would be very helpful.

Thanks
 
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Find a table of ideal gas properties for air that list T, h and Pr. Pr is the relative pressure for air when S2-S1=0 (constant entropy). Find h1, h2 and Pr1 from the table, h2s is tricky.

For the special case of air modeled as an ideal gas and S2-S1=0 this relation holds true:

P2/P1=Pr2/Pr1 solve for Pr2. Look up Pr2 in table and note corresponding h2s of about 443 Kj/Kg

From Fundamentals of Engineering Thermo. Moran and Shapiro edition 4, P. 276
 

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Thank you for your response AM. I appreciate it and will work through the steps.
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