(a) Explanation The below figure shows the p − V diagram of the process. Figure-(1) Write the expression for temperature at state 2. T 2 = ( V 1 V 2 ) n − 1 × T 1 (I) Here, the volume at state 1 is V 1 , the volume at state 2 is V 2 , the temperature at state 1 is T 1 and the polytropic index is n . Write the expression for the temperature at state 4. T 4 = ( V 3 V 4 ) n − 1 × T 3 (II) Here, the volume at state 3 is V 3 , the volume at state 4 is V 4 and the temperature at state 3 is T 3 . Write the expression for work done in the process 1-2. W 1 − 2 m = R ( T 2 − T 1 ) 1 − n (III) Write the expression for heat transfer in the process 1-2. Q 1 − 2 m = ( u 2 − u 1 ) + W 1 − 2 m (IV) Here, the internal energy at state 2 is u 2 and the internal energy at 1 is u 1 . Write the expression for heat transfer for the process 2-3. Q 2 − 3 m = u 3 − u 2 (V) Here, the internal energy at state 3 is u 3 . Write the expression for work done in the process 3-4. W 3 − 4 m = R ( T 4 − T 3 ) 1 − n (VI) Here, the temperature at state 4 is T 4 . Write the expression for heat transfer for the process 3-4. Q 3 − 4 m = ( u 4 − u 3 ) + W 3 − 4 m (VII) Write the expression for heat transfer in the process 4-1. Q 4 − 1 m = ( u 1 − u 4 ) (VIII) Conclusion: Substitute 10 for V 1 V 2 , 1.3 for n and 310 K for T 1 in Equation (I). T 2 = ( 10 ) 1.3 − 1 × ( 310 K ) = ( 10 ) 0.3 × ( 310 K ) = 618.53 K Substitute 1 10 for V 3 V 4 , 1.3 for n and 2200 K for T 3 in Equation (II). T 3 = ( 1 10 ) 1.3 − 1 × ( 2200 K ) = ( 0.1 ) 0.3 × ( 2200 K ) = 1102.61 K Substitute 618.53 K for T 2 , 310 K for T 1 , 0.287 KJ / kgK for R and 1.3 for n in Equation (III). W 1 − 2 m = ( 0.287 kJ / kgK ) ( 618.53 K − 310 K ) 1 − 1.3 = ( 0.287 kJ / kgK ) ( 308.53 K ) − 0.3 = 88.5481 kJ / kg − 0.3 = − 295.16 kJ / kg Thus, the work done in the process 1-2 is − 295.16 kJ / kg . Refer table A-22E “Ideal gas properties of air” to obtain the internal energy at 1 at temperature 310 K as u 1 = 221.25 kJ / kg . Refer table A-22E “Ideal gas properties of air” to obtain the internal energy at 2 at temperature 618.53 K as u 2 = 448.96 kJ / kg . Refer table A-22E “Ideal gas properties of air” to obtain the internal energy at 2 at temperature 2200 K as u 3 = 1872 (b) To determine The thermal efficiency. (c) To determine The mean effective pressure.

Appendices to accompany Fundamentals of Engineering Thermodynamics, 8e

8th Edition

ISBN: 9781118957219

Author: Michael J. Moran, Howard N. Shapiro

Publisher: WILEY

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Chapter 9.14, Problem 13P

(a)

To determine

The heat transfer in each process.

The work transfer in each process.

(b)

To determine

The thermal efficiency.

(c)

To determine

The mean effective pressure.

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Chapter 9.14, Problem 12P

Chapter 9.14, Problem 14P

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Appendices to accompany Fundamentals of Engineering Thermodynamics, 8e

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The heat transfer in each process. The work transfer in each process.

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The heat transfer in each process. The work transfer in each process.

The thermal efficiency.

The mean effective pressure.

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Chapter 9 Solutions

The heat transfer in each process.

The work transfer in each process.