GATE Thermodynamics Book

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THERMODYNAMICS

for

Mechanical Engineering

By

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Syllabus Thermodynamics

.

THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th_{Cross, 10}th_{Main, Jayanagar 4}th_{Block, Bangalore-11} : 080-65700750,  [email protected] © Copyright reserved. Web: www.thegateacademy.com

Syllabus for Thermodynamics

Zeroth, First and Second laws of thermodynamics; thermodynamic system and processes; Carnot cycle. irreversibility and availability; behaviour of ideal and real gases, properties of pure substances, calculation of work and heat in ideal processes; analysis of thermodynamic cycles related to energy conversion.

Power Engineering: Steam Tables, Rankine, Brayton cycles with regeneration and reheat. I.C. Engines: air-standard Otto, Diesel cycles. Refrigeration and air-conditioning: Vapour refrigeration cycle, heat pumps, gas refrigeration, Reverse Brayton cycle; moist air: psychrometric chart, basic psychrometric processes.

Analysis of GATE Papers

(Thermodynamics)

Year Percentage of marks Overall Percentage

2013 10.00 13.22% 2012 12.00 2011 19.00 2010 12.00 2009 12.00 2008 16.00 2007 10.67 2006 11.33 2005 16.00

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Contents Thermodynamics

THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th_{Cross, 10}th_{Main, Jayanagar 4}th_{Block, Bangalore-11} : 080-65700750,  [email protected] © Copyright reserved. Web: www.thegateacademy.com Page i

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Chapter

Page No.

#1. Basic Thermodynamics

1 – 42

 Thermodynamics Systems 1 – 2

 Thermodynamics processes 3 – 6

 Zeroth Law of Thermodynamics 6 – 7

 Work and Heat Transfer 7 – 10

 First Law of Thermodynamics 10 – 15

 Second Law of Thermodynamics 15 – 17

 Solved Examples 17 – 28

 Assignment - 1 29 – 33

 Answer Keys 35

 Explanations 35 – 42

#2. Properties of Gases and Pure Substances

43 – 71

 Properties of Pure substances 43 – 47

 Properties of Gases 47 – 50  Solved Examples 50 – 60  Assignment - 1 61 – 63  Assignment - 2 64  Answer Keys 65  Explanations 65 – 71

#3. Entropy Availability and Irreversibility

72 – 106

 Entropy 72 – 79

 Availability and Irreversibility 79 – 83

 Solved Examples 84 – 95

 Answer Keys 100

 Explanations 100 – 106

#4. Thermodynamics Cycles and Property Relations

107 – 129

 Thermodynamic Cycles 107 – 110

 Thermodynamic relations 110 – 113

 Joule Thomson Coeffficient 113 – 114

 Solved Examples 115 – 121  Assignment - 1 122 – 123  Assignment - 2 123 – 124  Answer Keys 125  Explanations 125 – 129

#5. Power Engineering

130 – 179

 Vapour Power Cycles 130 – 137

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Contents Thermodynamics

THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30th_{Cross, 10}th_{Main, Jayanagar 4}th_{Block, Bangalore-11} : 080-65700750,  [email protected] © Copyright reserved. Web: www.thegateacademy.com Page ii

 Impulse Turbines 139 – 140  Important Formulae 141  Solved Examples 142 – 158  Assignment - 1 159 – 163  Assignment - 2 163 – 165  Answer Keys 166  Explanations 166 – 179

#6. Internal Combustion Engines

180 – 220

 Introduction 180

 Basic of I.C Engine 180 – 185

 Air Standard Cycles 185 – 190

 Solved Examples 191 – 207  Assignment - 1 208 – 211  Assignment - 2 211 – 212  Answer Keys 213  Explanations 213 – 220

#7. Refrigeration

221 – 272

 Refrigeration 221 – 224

 COP of Vapor compression cycle 224 – 228

 Solved Examples 229 - 248  Assignment - 1 249– 254  Assignment - 2 254 – 256  Answer Keys 257  Explanations 257 – 272

#8. Psynchrometrics

273 – 305

 Psychrometry 273 – 275  Applications of Psychrometry 275 – 285  Solved Examples 286 – 292  Assignment - 1 293 – 295  Assignment - 2 295 – 296  Answer Keys 297  Explanations 297 -305

Module Test

306 – 334



Test Questions

306 – 317



Answer Keys

318 -



Explanations

318 – 334

Appendix

335 – 354

Reference Books

355

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Chapter 1 Thermodynamics

THE GATE ACADEMY PVT.LTD. H.O.: #74, KeshavaKrupa (third Floor), 30th Cross, 10th Main, Jayanagar 4th Block, Bangalore-11 : 080-65700750,  [email protected] © Copyright reserved. Web: www.thegateacademy.com Page 1

CHAPTER 1 Basic Thermodynamics

Thermodynamic Systems

A system is defined as a quantity of matter or a region in space chosen for study. The mass or region outside the system is called the surroundings. The real or imaginary surface that separates the system from its surroundings is called the boundary. The boundary of a system can be fixed or movable.

Systems may be considered to be closed or open, depending on whether a fixed mass or a fixed volume in space is chosen for study. A closed system (also known as a control mass or just system when the context makes it clear) consists of a fixed amount of mass and no mass can cross its boundary. That is, no mass can enter or leave a closed system, as shown in Fig. 1. But energy, in the form of heat or work, can cross the boundary and the volume of a closed system does not have to be fixed. If, as a special case, even energy is not allowed to cross the boundary, that system is called an isolated system.

Figure 1 Mass cannot cross the boundaries of closed, but energy can.

An open system or a control volume as it is often called, is a properly selected region in space. It usually encloses a device that involves mass flow such as a compressor, turbine or nozzle. Flow through these devices is best studied by selecting the region within the device as the control volume as shown in Fig 2. Both mass and energy can cross the boundary of a control volume. A large number of engineering problems involve mass flow in and out of a system and therefore, are modelled as control volumes. In general, any arbitrary region in space can be selected as a control volume. The boundaries of a control volume are called a control surface and they can be real or imaginary.

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Figure 2 An open system (a control volume) with one inlet and one exit

Any characteristic of a system is called a property. Some familiar properties are pressure P, temperature T, volume V and mass m. The list can be extended to include less familiar ones such as viscosity, thermal conductivity, modulus of elasticity, thermal expansion coefficient, electric resistivity and even velocity and elevation.

Properties are considered to be either intensive or extensive. Intensive properties are those that are independent of the mass of a system, such as temperature, pressure and density. Extensive properties are those whose values depend on the size—or extent—of the system. Total mass, total volume and total momentum are some examples of extensive properties. An easy way to determine whether a property is intensive or extensive is to divide the system into two equal parts with an imaginary partition, as shown in Fig. 3. Each part will have the same value of intensive properties as the original system, but half the value of the extensive properties.

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Thermodynamic Processes

Any change that a system undergoes from one equilibrium state to another is called a process and the series of states through which a system passes during a process is called the path of the process (Fig.4). To describe a process completely one should specify the initial and final states of the process, as well as the path it follows, and the interactions with the surroundings. When a process proceeds in such a manner that the system remains infinitesimally close to an equilibrium state at all times, it is called a static or equilibrium, process. A quasi-equilibrium process can be viewed as a sufficiently slow process that allows the system to adjust itself internally so that properties in one part of the system do not change any faster than those at other parts. It should be pointed out that a quasi-equilibrium process is an idealized process and is not a true representation of an actual process. These processes are analyzed using process diagrams. Process diagrams plotted by employing thermodynamic properties as coordinates are very useful in visualizing the processes. Some common properties that are used as coordinates are temperature T, pressure P and volume V (or specific volume v).

Figure 4 A process between states 1 and 2 and the process path

Some of the general thermodynamic processes are explained as under with the help of process diagrams.

Quasi – static process:

The departure of the state of the system from the thermodynamic equilibrium is infinitely small.

The quasi – static process is an ‘infinite slow’ process.

P V All are in thermodynamic equilibrium 1 2

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Thermodynamic processes (non-flow processes)

a)

Constant pressure or Isobaric process

PV = mRT P = constant(C) V ∝ T V T V T

b)

Constant volume process or Isochoric process

PV = mRT P = constant(C) P ∝ T P T P T

c)

Isothermal (constant temperature) process

P W = ∫ V T = C 1 2 V P 1 2 V = C W = ∫ pdv V P 1 2 P = C

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d)

Reversible Adiabatic or Isentropic process

PV constant 1) PV = Constant P P ( )

2) PV = mRT

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PV

r

_{= C (Adiabatic)}

T

V

T

V

e)

Polytropic process (generalized process)

PV const n – index of expansion n = ( ⁄ ) ( ⁄ ) 1) PVn_{= Constant} P P ( V V ) 2) TV T . V P V P = C 1 2 P V P = C 1 2

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Representation of thermodynamic processes on P – V diagram

Thermodynamic Process Index of expansion (n)

Constant volume (V = C) ∞

Constant pressure (P = C ) 0

Isothermal (T = C) 1

Polytrophic (PV c 1< n < 1.25 Reversible adiabatic (PV C r (= 1.4 )

Zeroth Law of Thermodynamics

Based on our physiological sensations, we express the level of temperature qualitatively with words like freezing cold, warm, hot and red-hot. However, we cannot assign numerical values to temperatures based on our sensations alone. Fortunately, several properties of materials change with temperature in a repeatable and predictable way and this forms the basis for accurate temperature measurement.

When a body is brought into contact with another body that is at a different temperature, heat is transferred from the body at higher temperature to the one at lower temperature until both bodies attain the same temperature. At that point, the heat transfer stops and the two bodies are said to have reached thermal equilibrium. The equality of temperature is the only requirement for thermal equilibrium.

P PV = C PV = C T C P C V . P V PVn_=C T = C P = C V = C PVn = C PVn_{= C} T=C P = C PVn_=C V=C

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