Lecture 29-30: Closed system entropy balance

ME 200 Thermodynamics I Spring 2016 Lecture 29-30: Closed system entropy balance Yong Li Shanghai Jiao Tong University Institute of Refrigeration and Cryogenics 800 Dong Chuan Road Shanghai, 200240, P. R. China Email : liyo@sjtu.edu.cn Phone: 86-21-34206056; Fax: 86-21-34206056 1.1

Last Lecture» Clausius inequality» Entropy change and entropy» Entropy Data for Water and Refrigerants» T ds equations» Entropy change for ideal gases A change in phase liquids and solids 1.2

Concept problems Does a cycle for which Why? violate the Clausius inequality?» No. The represents the net heat transfer during a cycle, which could be positive. A system undergoes a process between two fixed states first in a reversible manner and then in an irreversible manner. For which case is the entropy change greater? Why?» The entropy change will be the same for both cases since entropy is a property and it has a fixed value at a fixed state. Is the value of the integral states 1 and 2? Explain the same for all processes between» No. In general, that integral will have a different value for different processes. However, it will have the same value for all reversible processes 1.3

This Lecture Adiabatic internally reversible process, the entropy would be constant. A constantentropy process is called an isentropic process Internally reversible process can be represented as an area on a T S diagram Carnot power cycle Entropy Balance for Closed Systems Increase of Entropy Principle Entropy Rate Balance for Control Volumes 1.4

Concepts Entropy Change in Internally Reversible Processes A closed system undergoes an internally reversible process, its entropy can increase, decrease, or remain constant. Isentropic process ::: In an adiabatic internally reversible process, the entropy would be constant. It is a constant-entropy process. When a closed system undergoing an internally reversible process receives heat, the system experiences an increase in entropy. When heat transfer from the system, the entropy of the system decreases. An entropy transfer accompanies heat transfer. The direction of the entropy transfer is the same as that of the heat transfer. 1.5

Area Representation for Heat Transfer Heat transfer to a closed system during an internally reversible process can be represented as an area on a T S diagram.» T must be in kelvins» The area interpretation of heat transfer is not valid for irreversible processes 1.6

Carnot Cycles on the T S diagram. The cycle consists of four internally reversible processes in series Q 23 = T H (S 3 S 2 ) Q 41 = T C (S 1 S 4 ) S 1 =S 2 S 3 =S 4 Carnot power cycle 1.7

Example 1:Internally Reversible Process of Water Known: Water contained in a piston cylinder assembly undergoes an internally reversible process at 100 o C from saturated liquid to saturated vapor Find: the work and heat transfer per unit mass. Assumptions:» The water in the piston cylinder assembly is a closed system.» The process is internally reversible.» T and p are constant during the process.» PE=0, KE=0 1.8

Example 1:Internally Reversible Process of Water Known: Water contained in a piston cylinder assembly undergoes an internally reversible process at 100 o C from saturated liquid to saturated vapor 1.9

Entropy Change of a Substance in a Tank A rigid tank contains 5 kg of refrigerant-134a initially at 20 C and 140 kpa. The refrigerant is now cooled while being stirred until its pressure drops to 100 kpa. Determine the entropy change of the refrigerant during this process. The refrigerant is a saturated liquid vapor mixture at state 2 since v f <v 2 <v g at 100 kpa 1.10

Entropy Balance Closed System For closed systems, entropy change occurs only due to two mechanisms:» Entropy transfer due to heat exchange at every boundary of the system» Entropy generation (production) because of irreversibilities within the given system Entropy balance for closed system 1.11

Developing the Entropy Balance closed system entropy balance 1.12

Closed System Entropy Balance closed system entropy balance The second law requires that entropy production be positive, or zero, The change in entropy of the system may be positive, negative, or zero Like other properties, entropy change can be determined without knowledge of the details of the process. 1.13

Illustration of the Entropy Transfer and Entropy Production The reservoir is free of irreversibility The system is with irreversibilities, friction, other Entropy balance for the system Heat transfer reverse, the magnitude of the entropy transfer the same, direction reversed. The entropy of the system might decrease 1.14 No entropy transfer associated with work.

Other Forms of the Entropy Balance Heat transfer takes place at several locations on the boundary of a system On a time rate basis, the closed system entropy rate balance Differential form no internal irreversibilities 1.15

Example 1: Entropy Generation during Heat Transfer Processes Determine which heat transfer process is more irreversible Q S T Adiabatic Q=0 S (a) For the heat transfer to a sink at 500 K: (b) For the heat transfer to a sink at 750 K: S source S sink S source S sink 1.16

Example 2: Irreversible Process of Water Known: Water initially a saturated liquid saturated vapor at 100 o C, no heat transfer, action of a paddle wheel Find: Determine the net work per unit mass and the entropy produced per unit mass. Assumptions:» Closed system, Adiabatic.» system is at an equilibrium state» no change in KE or PE Analysis: Table A-2 at 100 o C for s Entropy production in Example 6.1 is 0. Here, fluid friction cause > 0 1.17

Example 3: Evaluating Minimum Theoretical Compression Work Known: Refrigerant 134a is compressed without Q from 0 o C saturated vapor to 0.7 MPa. Find: Determine the minimum theoretical work input required per unit of mass. Assumptions:.. Analysis: Table A-10 Table A-12 at 0.7 MPa, with s 2s =s 1 =0.9190 kj/kgk, u 2s = 244.32 kj/kg The minimum work input 1.18

Example 4: Entropy Generation in a Wall Known: steady heat transfer through a 5-m*7-m brick wall of a house of thickness 30 cm. On a day when the temperature of the outdoors is 0C, the house is maintained at 27C. The temperatures of the inner and outer surfaces of the brick wall are measured to be 20C and 5C, respectively, and the rate of heat transfer through the wall is 1035 W Find: the rate of entropy generation in the wall, and the rate of total entropy generation associated with this heat transfer process Assumptions: 1. steady process, 2. 1-D heat transfer Analysis: 1035 W 1.19

Home work Problems:» 逻辑 : 推论和证明的思想过程 valid reasoning» Write out the logic of our textbook Ch1~Ch6 in a A4 paper. Include a diagram with concepts and equations 1.20