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Fundamentals of Thermal-Fluid Sciences
Yunus A. Çengel, Robert H. Turner, John M. Cimbala McGraw-Hill

Week 6-7 (Chapter 8) ENTROPY
KHAIRUL FADZLI BIN SAMAT Faculty of Manufacturing Engineering Universiti Teknikal Malaysia Melaka

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Boltzmann relation

A pure crystalline substance at absolute zero temperature is in perfect order, and its entropy is zero (the third law of thermodynamics).

The level of molecular disorder (entropy) of a substance increases as it melts or evaporates.

Disorganized energy does not create much useful effect, no matter how large it is. 2

The paddle-wheel work done on a gas increases the level of disorder (entropy) of the gas, and thus energy is degraded during this process. In the absence of friction, raising a weight by a rotating shaft does not create any disorder (entropy), and thus energy is not degraded during this process. During a heat transfer process, the net entropy increases. (The increase in the entropy of the cold body more than offsets the decrease in the entropy of the hot body.) 3


Clausius inequality

Formal definition of entropy

The system considered in the development of the Clausius inequality.

The equality in the Clausius inequality holds for totally or just internally reversible cycles and the inequality for the irreversible ones. 4

A quantity whose cyclic integral is zero (i.e., a property like volume) Entropy is an extensive property of a system.

The net change in volume (a property) during a cycle is always zero. A Special Case: Internally Reversible The entropy change between two specified states is the same whether the process is reversible or irreversible.

Isothermal Heat Transfer Processes

This equation is particularly useful for determining the entropy changes of thermal energy reservoirs. 5

Example 1: Entropy Change during an Isothermal Process
• A piston cylinder device contains a liquid-vapor mixture of water at 300 K. During a constant-pressure process, 750 kJ of heat is transferred to the water. As a result, part of the liquid in the cylinder vaporizes. Determine the entropy change of the water during this process. Solution: Q T system 750 kJ  2.5kJ / K 300 K

S sys,isothermal 



The equality holds for an internally reversible process and the inequality for an irreversible process.

A cycle composed of a reversible and an irreversible process. Some entropy is generated or created during an irreversible process, and this generation is due entirely to the presence of irreversibilities. The entropy generation Sgen is always a positive quantity or zero. Can the entropy of a system during a process decrease? 7

The entropy change of an isolated system is the sum of the entropy changes of its components, and is never less than zero. A system and its surroundings form an isolated system. The increase of entropy principle 8

Some Remarks about Entropy
1. Processes can occur in a certain direction only, not in any direction. A process must proceed in the direction that complies with the increase of entropy principle, that is, Sgen ≥ 0. A process that violates this principle is impossible. 2. Entropy is a nonconserved property, and there is no such thing as the conservation of entropy principle. Entropy is conserved during the idealized reversible processes only and increases during all actual processes. 3. The performance of engineering systems is degraded by the presence of irreversibilities, and entropy generation is a measure of the magnitudes of the irreversibilities during that process. It is also used to establish criteria for the performance of engineering devices. 9

The entropy change of a system can be negative, but the entropy generation cannot.

Entropy is a property, and thus the value...
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