CH2123: You find an interesting expression for entropy generation during an irreversible compression in terms of efficiency: Chemical Thermodynamics Home Work, NTU, Singapore

Question 1

You find an interesting expression for entropy generation during an irreversible compression in terms of efficiency (η), the ratio of pressures, and γ. The expression is valid for ideal gases with constant, temperature independent,

• For rp = 5, plot Sgen for an ideal monoatomic, diatomic, and polyatomic gas versus efficiency (0.5 ≤ η ≤ 1). You can draw a rough sketch of your plot in your answers. At a given efficiency, which gas has the lowest entropy generated?
• Simply by observing the terms in the equation for Sgen, can you rationalize which monoatomic, diatomic, or polyatomic gases will have the lowest entropy generation at a given efficiency and rp? Explain in 2-4 sentences.
• An adiabatic compressor having efficiency η, operates at a steady state between an inlet condition of T1, P1, and an outlet condition of P2. Derive the relationship between Sgen (entropy generated) and η shown above. The fluid behaves like an ideal gas with temperature-independent heat capacities Cp, and Cv.

Question 2

Demonstrate using mathematical equations that the power requirement for compressing a gas is smaller, the more complex the gas. Assuming fixed values for the molar flow rate, efficiency, T1, P1, and P2, and that the gas is ideal with heat capacities that are independent of temperature.

Question 3

A steam power plant employs two adiabatic turbines in series. Steam enters the first turbine at 923.15 K, 7000 kPa, and discharges from the second turbine at 20 kPa. The system is designed for equal power outputs from the two turbines, based on a turbine efficiency of 75% for each turbine. Please use steam tables.

• Determine the temperature and pressure of the steam in its intermediate state between the two turbines.
• What is the overall efficiency of the two turbines together with respect to the isentropic expansion of the steam from the initial to the final state?