Explanation The p - v diagram for the Otto cycle is shown below. Figure-(1) The following figure shows the T - s diagram for the Otto cycle. Figure-(1) Write the expression for relation between, temperature and compression ratio for process 1-2. T 1 T 2 = r c γ − 1 (I) Here, the temperature at compressor outlet is T 2 , the compressor inlet is T 1 and the compression ratio is r c . Write the expression for relation between, temperature and compression ratio for process 3-4. T 3 T 4 = r c γ − 1 (II) Here, the temperature after expansion of the charge is T 4 , before expansion of the charge is T 3 and the compression ratio is r c . Write the expression for the net work of the cycle. W n e t = c v ( T 3 − T 2 + T 1 − T 4 ) (III) Here, the specific heat of the air at constant volume is c v . Write the expression for the thermal efficiency for the Otto Cycle. η o t t o = 1 − 1 r c γ − 1 (IV) Here, the compression ratio is r c and the adiabatic index is γ . Write the expression for the volume at inlet of the compressor. V 1 = R T 1 p 1 (V) Here, the gas constant is R . Write the expression for the compression ratio. r c = V 1 V 2 (VI) Here, the volume at inlet of the compressor is V 1 and at outlet is V 2 . Write the expression for the swept volume. V s = V 1 − V 2 (VII) Write the expression for the mean effective pressure. m e p = W c y c l e V s (VIII) Conclusion: For r c = 2 : Substitute 300 K for T 1 and 2 for r c and 1.4 for γ in Equation (I). T 2 300 K = 2 1.4 − 1 T 2 = ( 300 K ) × 1.32 T 2 = 396 K Substitute 2000 K for T 3 and 2 for r c and 1.4 for γ in Equation (II). 2000 K T 4 = 2 1.4 − 1 T 4 = 2000 K 1.32 T 4 = 1515.15 K Substitute 0.718 kJ / kg ⋅ K for c v , 2000 K for T 3 , 1515.15 K for T 4 , 396 K for T 2 , 300 K for T 1 in Equation.(III). W n e t = ( 0.718 kJ / kg ⋅ K ) ( 2000 K − 396 K + 300 K − 1515.15 K ) = ( 0.718 kJ / kg ⋅ K ) × 389 K = 279.3 kJ / kg Substitute 2 for r c and 1.4 for γ in Equation (IV). η o t t o = 1 − 1 2 1.4 − 1 = 1 − 0.7578 = 0.242 = 24.2 % For r c = 14 : Substitute 300 K for T 1 and 14 for r c and 1.4 for γ in Equation (I). T 2 300 K = 14 1.4 − 1 T 2 = ( 300 K ) × 2.87 T 2 = 861 K Substitute 2000 K for T 3 and 14 for r c and 1.4 for γ in Equation (II). 2000 K T 4 = 14 1.4 − 1 T 4 = 2000 K 2.87 T 4 = 697 K Substitute 0.718 kJ / kg ⋅ K for c v , 2000 K for T 3 , 697 K for T 4 , 861 K for T 2 , 300 K for T 1 in Equation

8th Edition

ISBN: 9781119391630

Author: MORAN

Publisher: WILEY

See similar textbooks

Question

Chapter 9.14, Problem 15P

To determine

The plot of net work per unit mass versus compression ratio.

The plot of thermal efficiency versus compression ratio.

The plot of mean effective pressure versus compression ratio.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.14, Problem 14P

Chapter 9.14, Problem 16P

Students have asked these similar questions

A continuous flow calorimeter was used to obtain the calorific value of a sample of fuel and the following data collected: Mass of fuel: 2.25 kgInlet water temperature: 11 ° COutlet water temperature 60 ° CQuantity of water: 360 Liters Calorimeter efficiency: 85%Calculate the calorific value of the sample ( kJ / kg ). ive submitted this question twice and have gotten two way different answers. looking for some help thanks

15 kg of steel ball bearings at 100 ° C is immersed in 25 kg of water at 20 ° C . Assuming no loss of heat to or from the container, calculate the final temperature of the water after equilibrium has been attained.Specific heat of steel: 0.4857 kJ / kg / ° KSpecific heat of water: 4.187 kJ / kg / ° K

Sketch and explain a PV Diagram and a Temperature Entropy Diagram for a 4 stroke diesel engine

Chapter 9 Solutions

FUND OF ENGINEERING THERMO W/WILEY PLU

Ch. 9.14 - Prob. 1E Ch. 9.14 - Prob. 2E Ch. 9.14 - Prob. 3E Ch. 9.14 - Prob. 4E Ch. 9.14 - Prob. 5E Ch. 9.14 - 6. What is the purpose of a rear diffuser on a...Ch. 9.14 - 7. What is the meaning of the octane rating that...Ch. 9.14 - Prob. 8E Ch. 9.14 - Prob. 9E Ch. 9.14 - 10. What is the purpose of the gas turbine–powered...

Knowledge Booster

The plot of net work per unit mass versus compression ratio. The plot of thermal efficiency versus compression ratio. The plot of mean effective pressure versus compression ratio.

The plot of net work per unit mass versus compression ratio. The plot of thermal efficiency versus compression ratio. The plot of mean effective pressure versus compression ratio.

Want to see the full answer?

Chapter 9 Solutions

The plot of net work per unit mass versus compression ratio.

The plot of thermal efficiency versus compression ratio.

The plot of mean effective pressure versus compression ratio.