# Chapter 6 - Chapter 6 Using Entropy Clausius Inequality...

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Chapter 6 Using Entropy Clausius Inequality Considering a system receives energy Q at its boundary at temperature T from a thermal reservoir at res T and develops work W . By introducing an intermediary reversible cycle which receiving Q from the reservoir and supplies Q to the system while producing work W , the heat transfer between the system and the reservoir is sure not to present any irreversibility of any kind. Since the intermediary cycle is reversible, then b res T Q T Q , and from energy balance the energy change of combined cycle (intermediary cycle + system) C C W Q dE where W W W C . C b res C dE T Q T W 0 b res C b res C T Q T dE T Q T W 0 b T Q When there are no irreversibilities within the system, 0 b T Q When there are irreversibilities within the system, 0 b T Q Or, it can be expressed as cycle b T Q 1

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where cycle can be viewed as a measure of the effect of the irreversibilities present with the system executing the cycle, and the values 0 cycle , no irreversibilities present within the system. 0 cycle , irreversibilities present within the system. 0 cycle , impossible . Entropy Change Assuming processes A, B, and C for a closed system between state 1 and state 2 are all reversible. Considering these two cycles, 1 2 1   C A : 0 1 2 2 1 cycle C A T Q T Q 1 2 1   C B : 0 1 2 2 1 cycle C B T Q T Q B A T Q T Q 1 2 2 1 The integral of T Q has the same value for any internally reversible process between the two states. In other words, the value of the integral depends on the end states only. The integral of T Q represents the change in some property of the system. Entropy ( S ), an extensive property (J/K or Btu/ R). rev T Q S S int 2 1 1 2 rev T Q dS int The above equation allows the determination of the change in entropy, and once it has been evaluated, this is the magnitude of the entropy change for all processes of the system between the two states. Entropy ( S ) is a property, the change in entropy of a system in going from one state to another is the same fro all processes, both internally reversible and irreversible, between these two states.
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