Explanation Draw P − v for dual cycle as shown in Figure (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 Here, specific heat ratio is k , the compression ratio is r , the specific heat ratio is k , volume at state 1 is ν 1 and volume at state 2 is ν 2 . Write the temperature, and pressure relation for the constant volume heat addition process 2 − x . T x = T 2 ( P x P 2 ) = T 2 ( r p ) (I) Here, temperature at state x is T x , temperature at state 2 is T 2 , pressure at state x is P x and pressure at state 2 is P 2 . Write the temperature, and volume relation for the constant pressure heat addition process x − 3 . T 3 = T x ( ν 3 ν x ) = T x r c (II) Here, the cutoff ratio is r c , volume at state 3 is ν 3 and volume at state x is ν x . Application first law to the process 2 − x . q 2 − x = c v ( T x − T 2 ) Here, the heat input to the process 2 − x is q 2 − x and specific heat at constant volume is c ν . Application of first law to the process x − 3 . q x − 3 = c p ( T 3 − T x ) Here, specific heat at constant pressure is c p , and the work done by the process x − 3 is Write the expression to obtain the net heat addition to the cycle ( q in ) . q in = q 2 − x + q x − 3 (III) Conclusion: Substitute c p ( T 3 − T x ) for q x − 3 and c v ( T x − T 2 ) for q 2 − x in Equation (III). q in = c v ( T x − T 2 ) + c p ( T 3 − T x ) (IV) Substitute T 1 ( r ) k − 1 for T 2 in Equation (I)

9th Edition

ISBN: 9781266657610

Author: CENGEL

Publisher: MCG CUSTOM

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 182RP

To determine

Derive the equation for qincvT1(r)k−1 in terms of k,rc and rp.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.12, Problem 181RP

Chapter 9.12, Problem 192FEP

Students have asked these similar questions

IMPORTANT: For problem solving items, start your solution by presenting the cycle in P-v and T-s diagrams. Label all points and mark the process where the heat is added and rejected. Also mark the area showing the net work of the cycle. The parameters of the initial state of one kilogram of air in the cycle of an internal combustion engine are o.095 MPa and 65 deg.C. The compression ratio is 12. Compare the values of the thermal efficiency for isobaric and isometric heat supply in the amounts of 820 kJ.

Steam is delivered to turbine at 5.4 MPa and 600 degree C. Before condensation at 31 degree C, steam is extracted for feed water heating at 0.6 MPa. The turbine exhaust is 60 degree C. the required values of some state point properties are tabulated below. 10. Calculate the net work of the cycle.

The condensing pressure for a Rankine Engine is 1.6 bar. 200°C and the steam at the beginning of expansion is at 3.75 Mpa, 400°C. Calculate the efficiency of cycle and engine using the mollier chart. Draw P-V and T-S diagram. Can you show me the detailed step-by-step solution using the given formula?

Chapter 9 Solutions

THERMODYNAMICS (LL)-W/ACCESS >CUSTOM<

Ch. 9.12 - What are the air-standard assumptions?Ch. 9.12 - What is the difference between air-standard...Ch. 9.12 - Prob. 3P Ch. 9.12 - How does the thermal efficiency of an ideal cycle,...Ch. 9.12 - How are the combustion and exhaust processes...Ch. 9.12 - What does the area enclosed by the cycle represent...Ch. 9.12 - Prob. 7P Ch. 9.12 - Can the mean effective pressure of an automobile...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.

Derive the equation for q in c v T 1 ( r ) k − 1 in terms of k , r c and r p .

Solution Summary: The author calculates the equation for q_inc's equation, P-v, and the temperature and pressure relation for the isentropic compression process.

Concept explainers

Derive the equation for qincvT1(r)k−1 in terms of k,rc and rp.

Want to see the full answer?

Chapter 9 Solutions