当前位置:首页 >> 机械/仪表 >>

熵-英文版


Entropy (YAC- Ch. 6)
In this Chapter, we will: Introduce the thermodynamic property called Entropy (S) Entropy is defined using the Clausius inequality Introduce the Increase of Entropy Principle which states that
– the entropy for an isolated system (or a system plus its surroundings) is always increases or, at best, remains the same. – Second Law in terms of Entropy

Learn to use the Entropy balance equation: entropy change = entropy transfer + entropy change. Analyze entropy changes in thermodynamic process and learn how to use thermodynamic tables Examine entropy relationships (Tds relations), entropy relations for ideal gases. Property diagrams involving entropy (T-s and h-s diagrams)

Entrpy.ppt, 10/18/01

pages

Entropy – A Property
Entropy is a thermodynamic property; it can be viewed as a measure of disorder. i.e. More disorganized a system the higher its entropy. δQ Defined using Clausius inequality ≤0 ∫ T rev where δQ is the differential heat transfer & T is the absolute temperature at the boundary where the heat transfer occurs Clausius inequality is valid for all cycles, reversible and irreversible. Consider a reversible Carnot cycle: δ Q QH QL Q T Q T = , from Carnot efficiceny ηth = 1 L = 1 L , L = L ∫ T TH TL QH TH QH TH
Therefore,
δQ



δQ
T

= 0 for a reversible Carnot cycle

δQ ∫ T rev = 0

Since ∫ δ = 0, i.e. it does not change if you return to the same state, T rev it must be a property, by defintion: Let's define a thermodynamic property entropy (S), such that 2 2 δQ δQ True for a Reversible
dS = T , for any reversible process ∫ dS = ∫
1 1 rev

T

= S2 S1

rev

Process only

The change of entropy can be defined based on a reversible process

Entropy (cont'd)
Since entropy is a thermodynamic property, it has fixed values at a fixed thermodynamic states. Hence, the change, S, is determined by the initial and final state. BUT.. The change is = δQ only for a Reversible Process

∫ T



δQ

Consider a cycle, where Process 2-1 is reversible and 12 may or may not be reversible

δQ δQ = ∫ + ∫ ≤0 T 1 T 2 T rev δQ δQ δQ dS = 0 = ∫ =∫ + ∫ ∫ T rev 1 T rev 2 T rev
2 1 2 2

2

1

From entropy definition δQ dS= , T rev
2

T

any process

2

δQ δQ Therefore, ∫ ≤∫ = ∫ dS = S 2 S1 = S T 1 T rev 1 1 δQ S = S 2 S1 ≥ ∫ , This is valid for all processes T 1
2

1

reversible process

dS ≥

δQ

δQ δQ , since dS = , dS > T T rev T irrev

S

Increase of Entropy Principle (YAC- Ch. 6-3)
δQ S = S2 S1 ≥ ∫ , define entropy generation Sgen T 1
2

S system

δQ δQ = S2 S1 = ∫ + S gen ≥ ∫ T T 1 1
2 2

Increase of Entropy Principle

Entropy change Entropy Transfer
(due to heat transfer)

Entropy Generation

The principle states that for an isolated Or a closed adiabatic Or System + Surroundings A process can only take place such that Sgen≥ 0 where Sge = 0 for a reversible process only And Sge can never be les than zero. Implications: Entropy, unlike energy, is non-conservative since it is always increasing. The entropy of the universe is continuously increasing, in other words, it is becoming disorganized and is approaching chaotic. The entropy generation is due to the presence of irreversibilities. Therefore, the higher the entropy generation the higher the irreversibilities and, accordingly, the lower the efficiency of a device since a reversible system is the most efficient system. The above is another statement of the second law

Second Law & Entropy Balance (YAC- Ch. 6-4)
Increase of Entropy Principle is another way of stating the Second Law of Thermodynamics: Second Law : Entropy can be created but NOT destroyed (In contrast, the first law states: Energy is always conserved) Note that this does not mean that the entropy of a system cannot be reduced, it can. However, total entropy of a system + surroundings cannot be reduced Entropy Balance is used to determine the Change in entropy of a system as follows: Entropy change = Entropy Transfer + Entropy Generation where, Entropy change = S = S2 - S1 Entropy Transfer = Transfer due to Heat (Q/T) + Entropy flow due to mass flow (misi – mese) Entropy Generation = Sgen≥ 0 For a Closed System: S2 - S1 = ∑Qk /Tk + Sgen In Rate Form: dS/dt = ∑Qk /Tk + Sgen For an Open System (Control Volume):
dS cv Qk =∑ + ∑ m i s i ∑ m e s e + S gen,CV dt Tk

Similar to energy and mass conservation, the entropy balance equations can be simplified Under appropriate conditions, e.g. steady state, adiabatic….

Entropy Generation Example
Show that heat can not be transferred from the low-temperature sink to the hightemperature source based on the increase of entropy principle. Source 800 K Q=2000 kJ
S(source) = 2000/800 = 2.5 (kJ/K) S(sink) = -2000/500 = -4 (kJ/K) Sgen= S(source)+ S(sink) = -1.5(kJ/K) < 0 It is impossible based on the entropy increase principle Sgen≥0, therefore, the heat can not transfer from low-temp. to high-temp. without external work input If the process is reversed, 2000 kJ of heat is transferred from the source to the sink, Sgen=1.5 (kJ/K) > 0, and the process can occur according to the second law

Sink 500 K

If the sink temperature is increased to 700 K, how about the entropy generation? S(source) = -2000/800 = -2.5(kJ/K) S(sink) = 2000/700 = 2.86 (kJ/K) Sgen= S(source)+ S(sink) = 0.36 (kJ/K) < 1.5 (kJ/K) Entropy generation is less than when the sink temperature is 500 K, less irreversibility. Heat transfer between objects having large temperature difference generates higher degree of irreversibilities


相关文章:
...& Coding信息论与编码(英文版)第二章 信源熵-习题答...
Information Theory & Coding信息论与编码(英文版)第二章 信源-习题答案_计算机软件及应用_IT/计算机_专业资料。2.1 试问四进制、八进制脉冲所含信息量是二进...
熵的定义
熵的定义_理学_高等教育_教育专区。在诸多领域的应用,催生出许多理论 科技名词定义中文名称: 英文名称: entropy 定义 1: 表示物质系统状态的一个物理量(...
汉语信源与英语信源及其信息熵的研究
汉语信源、英语信源及其信息熵的研究【摘要】本文主要搜集资料,对目前在信息领域内对于汉语、英语这两大主流 语言的信源进行信息研究的资料进行了阅读和整合, ...
12-14年原题英文版及摘要翻译评价
12-14年原题英文版及摘要翻译评价_理学_高等教育_教育专区。美赛12年至14年...之后,应用法和线性加 权法来获取评价等级。 为了评估两个模型的准确性,定义...
信息熵个人总结超全
在吴军老 师那篇《汉语信息和语言模型的复杂度》文章里说,只考虑字频英文 是 4.46 比特/字符的信息,汉字是 9.6 比特/字符,直观上很容易理解,英 ...
英语信源汉语信源信息熵的研究
英语信源汉语信源信息熵的研究_工学_高等教育_教育专区。英语信源、汉语信源及其信息熵的研究摘要 英语信源和汉语信源是两种不同的自然语信源,而信息反映 了...
科学家已经发明了测量无序量, 它称作,也是混沌度,是内部无序结构的总量。 4:传播学中表示一种情境的不确定性和无组织性。 英文释义:The degree of ...
Information Theory & Coding信息论与编码(英文版)例2
Information Theory & Coding信息论与编码(英文版)例2_计算机软件及应用_IT/计算机...(0,1/5,1/5,1/5,1/5,1/5)对每种概率分布,其香浓分别为 H(p0)=...
同样 意思。 ”为 S 命名时[6] ,他选用字义为“转变”的希腊语“τροπη” ,还要求 S 在发 音和字形上要与德文的能量“Energie” (英文为 ...
熵的计算
熵的计算_计算机硬件及网络_IT/计算机_专业资料。熵的计算云南大学数学与统计学...英文个人简历模板 创意简历模板汇集 推理型题分析与总结240份文档 2015小学生寒假...
更多相关标签: