Advanced Engineering Thermodynamics - Notes PDF

Preview

Summary

Brief lecture notes...

Description

Prof.Dr. Nawaf H. Saeid

Advanced Engineering Thermodynamics

1

Lecture 1: Entropy Adopted from Chapter 7 of: Y. Çengel and M. Boles, Thermodynamics–An Engineering Approach.

Objectives: o To define entropy and calculate the entropy changes that take place during processes. o To examine isentropic processes, and develop the property relations for these processes. o To develop the isentropic efficiencies for various steady-flow devices. Entropy The second law of thermodynamics leads to the definition of a new prop erty called entropy, which is a quantitative measure of microscopic disorder for a system. The definition of entropy is based on the Clausius inequality, given by: 

 ≤0 

kJ⁄K

1

That is, the cyclic integral of δQ/T is always less than or equal to zero. This inequality is valid for all cycles, reversible or irreversible. If no irreversibilities occur within the system as well as the reversible cyclic device, then the cycle undergone by the combined system is internally reversible. Therefore: 

 =0    

kJK ⁄

It is known that any quantity whose cyclic integral is zero is a property. Therefore, new property can be defined and the name of this property is entropy. It is designated S and is defined as: =  or

     

 −  =   

  ! "#$ %&'

kJ⁄K ()⁄*



Recall that isothermal heat transfer p rocesses are internally reversible. Therefore, the entropy change of a system during an internally reversible isothermal heat transfer process can be determined by performing the integration as:  + − , =  Entropy can be viewed as a measure of molecular disorder, or molecular randomness. As a system becomes more disordered, the positions of the molecules become less predictable and the entropy increases. Thus, it is not surprising that the entropy of a substance is lowest in the solid p hase and

Prof.Dr. Nawaf H. Saeid

Advanced Engineering Thermodynamics

2

highest in the gas phase. From a microscopic point of view, the entropy of a system increases whenever the thermal randomness or disorder of a system increases. The entropy of a pure crystalline substance at absolute zero temperature is zero. This statement is known as the third law of thermodynamics. The 3 rd law of thermodynamics provides an absolute reference point for the determination of entropy.

The Increase of Entropy Principle Consider a cycle that is made up of two processes: process 1-2, which is arbitrary (reversible or irreversible), and process 2-1, which is internally reversible. From the Clausius inequality,  +

  ,

 ≤ 0 kJ⁄ K 

,       0 kJ⁄ K    +

The second integral in the previous relation is recognized as the entropy change S1 - S2. Therefore, +

  ,

  - ,  +  0 

which can be rearranged as: +

+   , .   ,

 3 

where the equality holds for an internally reversible process and the inequality for an irreversible process. The quantity +  , represents the entropy change of the system. For a reversible + process, it becomes equal to0, ⁄ , which represents the entropy transfer with heat. The entropy change of a closed system during an irreversible process is always greater than the entropy transfer. That is, some entropy is generated or created during an irreversible process due to the irreversibilities. The entropy generated during a process is called entropy generation and is denoted by Sgen. Noting that the difference between the entropy change of a closed system and the entropy transfer is equal to entrop y generation, eq. (3) can be rewritten as an equality as: +

+  ,    ,

  - 14 

Prof.Dr. Nawaf H. Saeid

Advanced Engineering Thermodynamics

3

Note that the entropy generation Sgenis always a positive quantity or zero. Its value depends on the process, and thus it is not a property of the system. For an isolated system (or simply an adiabatic closed system), the heat transfer is zero, and equation (3) reduces to: ∆45678 . 0 This equation can be expressed as the entropy of an isolated system during a process always increases or, in the limiting case of a reversible process, remains constant. In other words, it never decreases. This is known as the increase of entropy principle. Entropy Change of Pure S ubstances The entropy values in the property tables are given relative to an arbitrary reference state. In steam tables the entropy of saturated liquid sf at 0.01°C is assigned the value of zero. For refrigerant134a, the zero value is assigned to saturated liquid at -40°C. The entropy values become negative at temperatures below the reference value. The value of entropy at a specified state is determined just like any other property v , u and h. In the compressed liquid and sup erheated vapour regions, it can be obtained directly from the tables at the specified state. In the saturated mixture region, it is determined from: 9  9: - ;9...