Me_thermodynamics_final.pdf

MECHANICAL ENGINEERING FOR UPSC Engineering Services Examination, GATE, State Engineering Service Examination & Public Sector Examination. (BHEL, NTPC, NHPC, DRDO, SAIL, HAL, BSNL, BPCL, NPCL, etc.)

THERMODYNAMICS

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First Edition : 2017

Typeset at : IES Master Publication, New Delhi-110016

CONTENTS 1.

Basics of Thermodynamics and First law .................................................. 01–51

2.

Second Law of Thermodynamics ................................................................ 52–83

3.

Entropy ......................................................................................................... 84–126

4.

Availability and Irreversibility .................................................................. 127–149

5.

Pure Substrances ..................................................................................... 150–167

6.

Gases and Gaseous Mixtures ................................................................ 168–210

7.

Thermodynamic Relations ........................................................................ 211–231

8.

Compressible flow and Shocks ............................................................... 232-296

1 INTRODUCTION Introduction



It is the science dealing with energy (heat) and its conversion into work along change in properties of the system in equilibrium.



Word thermodynamics originated during men’s endeavor to convert heat into work i.e. during heat engine invention. It derived from two Greek words namely THERME means heat and DYNAMICS means power (force+velocity).



In the initial phase it was assumed that conversion of heat into work is all about thermodynamics. But later it was felt that every wake of our life is controlled by thermodynamics. Or in other words the basic fundamentals of thermodynamics are based upon the natural processes and observations that we feel in daily ife.



These common observations are natural processes. For example balance i.e. equilibrium, flow of heat from high temperature to low temperature, water flows from high elevation to low elevation, aging of life of living organism, conservation of energy etc.

p.dV work or Boundary Work



It is observed that all the above mentioned observations or processes have a directional sense and rhythm to occur in a direction.

Free Expansion



Based upon these natural processes and common observations, four LAWS OF THERMODYNAMICS are drived. So these laws have no mathematical back up and proved empirically only. Firmness of these laws are proved by their wide applications and still not violated. The four laws of thermodynamics are,

Types of System Microscopic and Macroscopic Approach Types of Thermodynamic Properties Thermodynamic Equilibrium Pure Substance Temperature Concept

First Law of Thermodynamics Unsteady Flow Processes

1. Zeroth Law of thermodynamics 2. First law of thermodynamics. 3. Second law of thermodynamics. 4. Third law of thermodynamics.

2 Chapter-1 : Basics of Thermodynamics and First law System Boundary

Thermodynamic system is defined as a quantity of matter or region in space upon which thermodynamic analysis is done for a particular problem.

System

Surroundings/ environment

Surrou ndings Everything outside the thermodynamic system is non as surroundings.

System Boundary The system and surrounding separating line or boundary is called system boundary. The boundary of system may be either fixed or moving. It may also be either real or imaginary.

TYPES OF SYSTEM Thermodynamics system are divided in three groups namely, (1) Closed System.

(2) Open system.

(3) Isolated System.

(1) Closed System or Control Mass

Energy Transfer : (Heat or work)

It is a system of fixed mass i.e. mass can not change or cross the system boundary but energy can cross. (The volume of closed system is changing i.e. cylinder piston machine) i.e. boundary is moving. Example:

Boundary System

Environment or Surroundings

(No mass/matter movement)

(i) A constant amount of matter in cylinder-piston system, here the mass of the system is constant and volume can change i.e. boundary moving, energy can transfer through conducting wall of system. (ii) A steel container containing fluid having no outlet – no material movement across the boundary but energy can transfer across conducting wall. (2) Open System or Control Volume In this system the energy as well as mass can cross the system boundary. Generally boundary is fixed and a specific region or space of system is selected for analysis purpose. Boundary

Mass

Energy System

Example: Compressor, pump, turbine etc. (3) Isolated System This system has no interaction with surrounding i.e. neither mass nor energy can transfer the system boundary. It is a fixed mass and fixed energy system e.g. coffee in insulated thermo flask, universe is itself an isolated system. This is a special case of close system. Regd. office : F-126, (Upper Basement), Katwaria Sarai, New Delhi-110016 Mob. : 8010009955, 9711853908

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Mechanical Engineering (Study Package) 3 X No energy transfer Surroundings

No mass/matter transfer X

System matrix System

Mass transfer Energy Transfer

Open system Closed

Yes No

Yes Yes

Isolated

No

No

Control Volume and Control Surface For the analysis of open system such as compressor and turbine, attention is focussed on a certain volume surrounding the machine called control volume enclosed by control surface. Here matter as well as energy can cross the control surface. Energy

Mass in

Work

Control Volume Mass out

Control Surface (dashed)

MICROSCOPIC AND MACROSCOPIC APPROACH Microscopic Approach Here the study is focussed at molecular level i.e behaviour of molecules is studied. This study is also known as statistical thermodynamics. This is done when the density is very low.

Macroscopic Approach When the density is high, the individual molecular study is not possible so it is done on whole system i.e. average of system, the study is called macroscopic and is also called classical thermodynamics.

Thermodynamic Properties To analyse a thermodynamic system, some variables are required such as volume, temperature, pressure etc. These variables are called properties of system. These are macroscopic in nature. These are the coordinates of system. When all the properties have definite value, the system is said to exist in definite state. Regd. office : F-126, (Upper Basement), Katwaria Sarai, New Delhi-110016 Mob. : 8010009955, 9711853908

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4 Chapter-1 : Basics of Thermodynamics and First law

TYPES OF THERMODYNAMIC PROPERTIES There are two types of thermodynamic propertetis (1) Intensive property These are independent of mass or size of system e.g. pressure, temperature, density, thermal conductivity, dielectric constant, thermal expansion coefficient etc. (2) Extensive Property These properties depend on mass or size of system. If system is divided into two parts all extensive properties are halved. e.g. volume, kinetic energy, potential energy etc. NOTE

Specific properties are intensive e.g. [extensive property per unit mass]. Energy per unit mass, volume per unit mass etc. But work and heat are not properties.

Some Important Points Units of Pressure: S.I. unit – pascal (Pa): 1 Pa = 1 N/m2-similarly kilopascal – 103 N/m2 Mega Pa = 106 N/m2 1 bar =

105 N/m2

Standard atmospheric.1 atm = 101.325 kPa = 1.013×105 N/m2 (Pa) The unit of 1 mm Hg Pressure is torr, 

1.0 torr = 133 Pa = 1 mm Hg

One gram mole of gas = Molecular weight (gm) of substance. e.g. one gram mole of oxygen = 32 gram oxygen.

Change of State An operation which brings change in one or more properties is called change of state.

Path The series of states during change of state is called path of change of state.

Process When the path of change of state is completely specified i.e. mode of change of stated again i.e. constant volume, constant pressure etc. It is called as process e.g. isobaric process, isothermal process etc.

Cycle

A

A series of changes of state or processes in such a way that the final state is same as initial is called as cycle.  

The change in property in a cycle is always zero because of same initial and final state. Minimum two processes are required for a cycle.

1 P B 2 V A  B - Process 1–2–1 cycle

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Mechanical Engineering (Study Package) 5 Quasi-Static Process A process which is carried out with infinitely small pressure gradient and slowly is called quasi-static process. Some points about it are, 

All the states on the process are equilibrium states.



Infinite slowness is the characteristic feature of this process.



A frictionless quasi-static process is a reversible process.



Quasi-means almost i.e. the process is almost static. P

P 1

1

State 1 & 2 are in Equilibrium states

Equilibrium states Quasi-static process

This process cannot be defined 2

2 V

V

Fast/Practical Process

Slow/Impractical Process

Here points 1 and 2 are in

Infinitely slow process

equilibrium so only coordinates of 1

(Impractical): All the points

and 2 can be determine but any

between 1 and 2 are in equilibrium.

other points in between has no

So has definite value.

meaning.

Reversible and Irreversible Processes The process is called a reversible process if it can be completely reversed. It implies that when carried out in the opposite direction the system follows the same succession of states as it followed in the forward direction. Thus, the system is restored to the initial conditions. In addition, the interactions between the system and the surroundings are also equal and opposite in direction. Hence, not only the system but the surroundings also are restored to the initial conditions. Accordingly, if a process is reversible, then when it is reversed, the system and the surroundings both come back to the original states, and no trace of the history of the forward process is left.

THERMODYNAMIC EQUILIBRIUM A system is said to be in thermodynamic equilibrium if it is in three types of equilibrium. (1) Mechanical Equilibrium Equality of force or pressure throughout system if the system is in equilibrium with environment, the pressure will be equal to atmospheric pressure. (2) Chemical Equilibrium Equality of chemical potenital i.e. no chemical reaction, no change of concentration i.e. no mass diffusion throughout the system. (3) Thermal Equilibrium Temperature is unirform throughout the system. Regd. office : F-126, (Upper Basement), Katwaria Sarai, New Delhi-110016 Mob. : 8010009955, 9711853908

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6 Chapter-1 : Basics of Thermodynamics and First law NOTE

If system is in thermodyanic equlibrium, there will be no change in any macroscopic property.

PURE SUBSTANCE A substance is pure if, 

Homogeneous in composition – Chemical composition of each part of system is same.



Homogeneous in chemical aggregation – Chemical compound in the system must be combined in the same way in every part of the system.



Invariable in chemical aggregation – Chemical compostion doesn’t change in time. Change in phase is possible here.



A pure substance does not have to be of a single chemical element or compound so a mixture of various chemical compounds also qualify a pure substance.

Example of pure substances Atmospheric air, steam–water mixture, combustoin products of fuel. But mixture of air and liquid air is not pure substance because relative proportion of oxygen and nitrogen are different in two phases. Homogeneous and Heterogeneous Systems Any substance in single phase e.g. mixture of air water vapour, water and nitric acid is called homogeneous system and if a system has more than one phase, it is called heterogeneous system.

TEMPERATURE CONCEPT 

Temperature is the property which differentiate between hot and cold body.



To understand this concept, temperature bears the relationship with thermodynamics, as forces with statics and velocity with dynamics.



In order to understand the quantitative measure of temperature, a reference body is selected in such a way that there should be a reference physical characterstic which vary with temperature.



The reference body is called as thermometer and characterstic as thermometric property.



The basis of temperature measurement is Zeroth law of thermodynamics.

Zeroth Law of Thermodynamics

B

“If a body A is in thermal equilibrium with body B and body B is in thermal equilibrium with body C, then A and C will be in thermal equilibrium”.

C

A

Temperature Measurement Method Before 1954 This method of temperature measurement was based upon two reference points namely ice point assigned value 0°C and steam point assigned value 100°C. Temperature (x) was assumed linear function of thermometric property x. 

(x) = ax + b.

...(i)

At ice point,

i(x) = axi + b

...(ii)

where ‘a’ and ‘b’ are conslants

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