Chapter_7_1

Chapter_7_1 - Student Study Guide for 5th edition of...

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Student Study Guide for 5 th edition of Thermodynamics by Y. A. Ç engel & M. A. Boles 7-1 Chapter 7-1 Chapter 7: Entropy: A Measure of Disorder Entropy and the Clausius Inequality The second law of thermodynamics leads to the definition of a new property called entropy, a quantitative measure of microscopic disorder for a system. Entropy is a measure of energy that is no longer available to perform useful work within the current environment. To obtain the working definition of entropy and, thus, the second law, let's derive the Clausius inequality. Consider a heat reservoir giving up heat to a reversible heat engine, which in turn gives up heat to a piston-cylinder device as shown below.
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Student Study Guide for 5 th edition of Thermodynamics by Y. A. Ç engel & M. A. Boles 7-2 Chapter 7-2 We apply the first law on an incremental basis to the combined system composed of the heat engine and the system. EE E QWWd E in out c Rr e v s y sc −= −+= δδδ () where E c is the energy of the combined system. Let W c be the work done by the combined system. Then the first law becomes δδ δ WW W QW d E cr e vs y s Rc c =+ If we assume that the engine is totally reversible, then δ δ Q T Q T QT Q T R R RR = = The total net work done by the combined system becomes δ δ WT Q T dE cR c =− Now the total work done is found by taking the cyclic integral of the incremental work. Q T dE c zz δ If the system, as well as the heat engine, is required to undergo a cycle, then
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Student Study Guide for 5 th edition of Thermodynamics by Y. A. Ç engel & M. A. Boles 7-3 Chapter 7-3 dE c z = 0 and the total net work becomes WT Q T cR = z δ If W c is positive, we have a cyclic device exchanging energy with a single heat reservoir and producing an equivalent amount of work; thus, the Kelvin-Planck statement of the second law is violated. But W c can be zero (no work done) or negative (work is done on the combined system) and not violate the Kelvin-Planck statement of the second law. Therefore, since T R > 0 (absolute temperature), we conclude Q T =≤ z δ 0 or δ Q T z 0 Here Q is the net heat added to the system, Q net . δ Q T net z 0 This equation is called the Clausius inequality. The equality holds for the reversible process and the inequality holds for the irreversible process.
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Student Study Guide for 5 th edition of Thermodynamics by Y. A. Ç engel & M. A. Boles 7-4 Chapter 7-4 Example 7-1 For a particular power plant, the heat added and rejected both occur at constant temperature and no other processes experience any heat transfer. The heat is added in the amount of 3150 kJ at 440 o C and is rejected in the amount of 1950 kJ at 20 o C. Is the Clausius inequality satisfied and is the cycle reversible or irreversible? δ δδ Q T Q T Q T Q T Q T Q T Q T kJ K kJ K kJ K kJ K net net in net out net in net out in in out out z zz F H G I K J + F H G I K J F H G I K J + F H G I K J F H G I K J + F H G I K J + F H G I K J + + F H G I K J −≤ 0 0 0 0 3150 440 273 1950 20 273 0 4 418 6655 0 2237 0 () ( ) (. . ) .
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Chapter_7_1 - Student Study Guide for 5th edition of...

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