Explanation Draw the given ideal dual cycle on P − v diagram as in Figure (1) Write the ideal gas equation to calculate the mass of air. m = P 1 ν 1 R T 1 (I) Here, mass of air is m , , gas constant is R and volume at state 1 is v 1 . Write the temperature and volume relation for the isentropic compression process 1-2. T 2 = T 1 ( ν 1 ν 2 ) k − 1 = T 1 ( r ) k − 1 (II) Here, the compression ratio is r , the specific heat ratio is k , temperature at state 1 is T 1 , temperature at state 2 is T 2 , volume at state 1 is v 1 and volume at state 2 is v 2 . Write the expression for the heat addition to the process 2 − x ( Q x-2,in ) . Q 2-x,in = m ( u x − u 2 ) = m c v ( T x − T 2 ) (III) Here, the specific heat at constant volume is c v , internal energy at state 2 is u 2 , internal energy at state x is u x and temperature at state x is T x . Write the expression for the heat addition to the process x − 3 ( Q x − 3 ,in ) . Q x − 3 ,in = m c v ( h 3 − h x ) = m c v ( T 3 − T x ) (IV) Here, enthalpy at state 3 is h 3 , enthalpy at state x is h x and temperature at state 3 is T 3 . Write the ideal gas relation for the process x − 3 . P 3 v 3 T 3 = P x v x T x v 3 T 3 = v x T x v 3 v x = T 3 T x (V) Here, volume at state x is v x , volume at state 3 is v 3 pressure at state x is P x . P x and P 3 are equal for the process x − 3 . Write the expression for temperature and volume relation for isentropic expansion process3-4. T 4 = T 3 ( ν 3 ν 4 ) k − 1 (VI) Here, temperature at state 4 is T 4 and volume at state 4 is v 4 . Write the expression for the heat rejected from the cycle ( Q out ) . Q out = m ( u 4 − u 1 ) = m c v ( T 4 − T 1 ) (VII) Here, the specific heat at constant volume is c v . Write the expression for the thermal efficiency of the cycle ( η t h ) . η t h = 1 − Q o u t Q i n (VIII) Here, heat input is Q i n . Conclusion: From Table A-2E, “Ideal-gas specific heats of various common gases”, obtain the following properties for air at room temperature. c v = 0.171 Btu / lbm ⋅ R c p = 0.240 Btu / lbm ⋅ R k = 1.4 From Table A-1E, “Molar mass, gas constant, and critical-point properties”, obtain the Value of gas constant ( R ) for air at room temperature as 0.3704 psia ⋅ ft 3 / lbm ⋅ R . Substitute 14.7 psia for P 1 , 98 in 3 for ν 1 , 0.3704 psia ⋅ ft 3 / lbm ⋅ R for R , and 120 ° F for T 1 in Equation (I). m = ( 14.7 psia ) ( 98 in 3 ) ( 0.3704 psia ⋅ ft 3 / lbm ⋅ R ) ( 120 ° F ) = ( 14

8th Edition

ISBN: 9781307434316

Author: CENGEL

Publisher: INTER MCG

See similar textbooks

Concept explainers

IC engines

The term "engine" indicates a mechanical device/machine used to convert input energy to a specific mechanical output. The input energy may be in the form of chemical energy, thermal energy, or so on and mechanical output is in the form of mechanical ener…

Question

Chapter 9.12, Problem 162RP

To determine

The thermal efficiency of the cycle.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.12, Problem 161RP

Chapter 9.12, Problem 163RP

Students have asked these similar questions

An Otto cycle uses air as its working fluid. The compression ratio of the cycle is 10. 1,800 kJ/kg of heat is added during the heat addition process. If the temperature and pressure at the end of compression are 444C and 2,168Kpa. Assume constant specific heats for the analysis, determine (a) the temperature and pressure at the end of each process, (b) the thermal efficiency of the process (c) the net Work of the cycle (d)mean effective pressure of the cycle.

Consider an ideal Ericsson cycle with air as the working fluid executed in a steady-flow system. Air is at 27°C and 120 kPa at the beginning of the isothermal compression process, during which 150 kJ/kg of heat is rejected. Heat transfer to air occurs at 950 K. Determine the maximum pressure in the cycle.

In a steam plant operating according to an ideal Rankine cycle, water vapor enters the turbine at a pressure of 3.0 MPa and a temperature of 600 oC and exits the turbine with a dryness of 100 kPa and 0.8. By removing heat from the condenser to the surrounding environment, the water is provided to be saturated liquid at 100 kPa. In this case, what would be the amount of heat released from the Condenser to the surrounding environment per unit mass?

Chapter 9 Solutions

THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I

Ch. 9.12 - What are the air-standard assumptions?Ch. 9.12 - What is the difference between air-standard...Ch. 9.12 - How does the thermal efficiency of an ideal cycle,...Ch. 9.12 - What does the area enclosed by the cycle represent...Ch. 9.12 - Prob. 5P Ch. 9.12 - Prob. 6P Ch. 9.12 - Can the mean effective pressure of an automobile...Ch. 9.12 - Prob. 8P Ch. 9.12 - What is the difference between spark-ignition and...Ch. 9.12 - Prob. 10P

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 thermal efficiency of the cycle.

Solution Summary: The author illustrates the thermal efficiency of the cycle by drawing the ideal gas equation to calculate the mass of air.

Concept explainers

The thermal efficiency of the cycle.

Want to see the full answer?

Chapter 9 Solutions