Explanation Write the expression for the isentropic efficiency of a compressor for an ideal gas ( η C ) . η C = h 2 s − h 1 h 2 − h 1 = c p ( T 2 s − T 1 ) c p ( T 2 − T 1 ) = ( T 2 s − T 1 ) ( T 2 − T 1 ) (I) Here, the specific heat at constant pressure is c p , enthalpy at state 1 is h 1 , enthalpy at state 2 is h 2 and enthalpy on isentropic condition 2 s is h 2 s , temperature at state 1 is T 1 , temperature at state 2 is T 2 and temperature on isentropic condition 2 s is T 2 s . Write the temperature and pressure relation ratio at the compressor exit for the isentropic condition. T 2 s = T 1 ( P 2 P 1 ) ( k − 1 ) / k Here, the specific heat ratio is k , pressure at state 2 is P 2 and pressure at state 1 is P 1 . Write the expression for the isentropic efficiency of a turbine for an ideal gas ( η T ) . η T = h 4 − h 3 h 4 s − h 3 = c p ( T 4 − T 3 ) c p ( T 4 s − T 3 ) = ( T 4 − T 3 ) ( T 4 s − T 3 ) (II) Here, the specific heat at constant pressure is c p , enthalpy at state 3 is h 3 , enthalpy at state 4 is h 4 and enthalpy on isentropic condition 4 s is h 4 s , temperature at state 4 is T 4 , temperature at state 3 is T 3 and temperature on isentropic condition 4 s is T 4 s . Write the temperature and pressure relation ratio at the compressor exit for the isentropic condition. T 4 s = T 3 ( P 4 P 3 ) ( k − 1 ) / k Here, the specific heat ratio is k , pressure at state 3 is P 3 and pressure at state 4 is P 4 . Conclusion: Substitute [ T 1 ( P 2 P 1 ) ( k − 1 ) / k ] for T 2 s in Equation (I)

8th Edition

ISBN: 8220100257056

Author: CENGEL

Publisher: YUZU

See similar textbooks

Videos

Question

Chapter 7.13, Problem 220RP

To determine

The compressor and turbine isentropic efficiencies as (P2P1)(k−1)/k−1(T2T1−1) and T4T3−1(P4P3)(k−1)/k−1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.13, Problem 218RP

Chapter 7.13, Problem 222RP

Students have asked these similar questions

The Brayton cycle (1–2–3–4–1) can be modeled as a closed cycle with air (ideal gas with known constant properties) with a mass flow rate of m˙ B = 60 kg/s. The minimum and maximum pressures of the Brayton cycle are known and equal p B min = 0.3 MPa and p B max = 1.6 MPa, as well as the absorbed power Q˙H = 50 MW and the minimum temperature (T1 = 25ºC) of the cycle. Knowing that all processes occur in devices that operate in steady state, calculate the following parameters for each cycle: ( A ). The temperature at all points; ( B ). The compression and expansion power of each Brayton-Rankine cycle, as well as the absorbed/rejected heat transfer rate. ( C ). The efficiencies of each cycle, as well as the overall efficiency of the combined cycle (The combined cycle efficiency is calculated from the sum of the net work of the cycles under the heat supplied to the combined cycle). ( D ). The entropies generated from each process, as well as the total entropy for each cycle. General data: R…

C. In an ideal gas turbine power device, the pressure ratio is 6, the temperature entering the compressor is 27°C, and the maximum allowable temperature of the turbine is 816°C. What is the efficiency of this power device when it is carried out in reversible operation? However, the specific ratio is 1.4. (a)20% (b)30% (c)40% (d)50%

The following two claims are made by salesmen about newly invented 2-phase adiabatic compressors. Salesman A: "It can compress steam with a quality of 0.1 from 100 kPa to saturated liquid at 400 kPa." Salesman B: "It can compress steam with a quality of 0.1 from 100 kPa to saturated liquid at 1000 kPa." a. Show both claims on a T-S (temperature vs. specific entropy) diagram. b. Which claim or claims are possible? c. Which claim or claims are impossible?

Chapter 7 Solutions

EBK THERMODYNAMICS: AN ENGINEERING APPR

Ch. 7.13 - Prob. 1P Ch. 7.13 - Does the cyclic integral of heat have to be zero...Ch. 7.13 - Is a quantity whose cyclic integral is zero...Ch. 7.13 - Prob. 4P Ch. 7.13 - Prob. 5P Ch. 7.13 - How do the values of the integral 12Q/T compare...Ch. 7.13 - The entropy of a hot baked potato decreases as it...Ch. 7.13 - When a system is adiabatic, what can be said about...Ch. 7.13 - Prob. 9P Ch. 7.13 - A pistoncylinder device contains helium gas....

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The compressor and turbine isentropic efficiencies as ( P 2 P 1 ) ( k − 1 ) / k − 1 ( T 2 T 1 − 1 ) and T 4 T 3 − 1 ( P 4 P 3 ) ( k − 1 ) / k − 1 .

Solution Summary: The author explains the isentropic efficiency of a compressor and turbine for an ideal gas.

Videos

The compressor and turbine isentropic efficiencies as (P2P1)(k−1)/k−1(T2T1−1) and T4T3−1(P4P3)(k−1)/k−1.

Want to see the full answer?

Chapter 7 Solutions