# ch07-lec - Learning Objectives 1. Apply the second law of...

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Learning Objectives 1. Apply the second law of thermodynamics to processes. 2. Define a new property called entropy to quantify the second-law effects. 3. Establish the increase of entropy principle. 4. Calculate the entropy changes that take place during processes for pure substances, incompressible substances, and ideal gases. 5. Examine a special class of idealized processes, called isentropic processes and develop the property relations for these processes. 6. Derive the reversible steady-flow work relations. 7. Develop the isentropic, or adiabatic, efficiencies of various steady- flow engineering devices. 8. Introduce and apply the entropy balance to various systems.

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7-1 Entropy Clausius Inequality To define the entropy, we will develop the Clausius inequality Consider the system to the right Applying the first law to the combined system we get E C is the energy of the combined system The combined work is The energy balance is now C E E E = - out in C R dE W W Q = - - sys rev δ sys rev W W W C + = C C R dE W Q = Rudolf Clausius
7-1 Entropy Clausius Inequality (cont.) If the engine is totally reversible then, The total work becomes Now, the total work done is found by taking the cyclic integral of the incremental work T Q T Q R R δ = C R C dE T Q T W - = from L H L H T T Q Q = rev - = C R C dE T Q T W

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7-1 Entropy Clausius Inequality (cont.) If the system, as well as the heat engine, is allowed to undergo a cycle then, Since energy is a property, the total work becomes If W C is positive, then there exist a cyclic device exchanging energy with a single heat reservoir and producing an equivalent amount of work Such a device violates the Kelvin-Planck statement of the second law = T Q T W R C δ 0 = C dE
7-1 Entropy Clausius Inequality (cont.) This indicates that W C has to be zero or negative to not violate the Kelvin-Planck statement Since T R > 0 and Q is the net heat added to the system ( Q net ) This is the Clausius inequality The inequality is valid for all thermodynamic cycles, reversible or irreversible 0 = T Q T W R C δ

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7-1 Entropy Clausius Inequality (cont.) If no irreversibilities occur within the system as well as the cyclic device, then the cycle undergone by the combined system will be internally reversible As a result, the cycle can be reversed, with all of the quantities having the same magnitude, but the opposite sign In the reverse case, W C has to be zero or positive to avoid violation of the Kelvin-Planck statement Therefore, to avoid violation of the Kelvin-Planck statement for both the forward and reverse case, W C, int rev = 0 , from which follows
7-1 Entropy Clausius Inequality (cont.) The conclusions are The equality in the Clausius inequality holds for a totally or just internally reversible cycle The inequality in the Clausius inequality holds for

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## This note was uploaded on 04/20/2010 for the course M E 320 taught by Professor Deinert during the Spring '08 term at University of Texas at Austin.

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ch07-lec - Learning Objectives 1. Apply the second law of...

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