td chapter 1

8/8/2019 Td Chapter 1

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1. Basic Concepts

1. Introduction

The economic prosperity of a nation is measured in terms of energy produced. It is due to energy that man dominates the universe.

Thermodynamics is a science of energy. It is based on observations in nature. It predicts the real behaviour of process in home and industry.

Thermodynamics is useful to all branches of engineering.Earlier attempts to produce energy by perpetual motions were discarded by the laws of thermodynamics. Heat can easily be produced by burning

the fuels. How much energy is converted into work? How to reduce the consumption of fuels? What is possibility of utilization of new sources of energy?Thermodynamics has been developed to answer above questions.

Thermodynamics is a Greek word. Thermo means heat and dynamics means mechanical power. Thermodynamics converts heat into

mechanical energy. Precisely, thermodynamics may be defined as a science which deals with energy transformation from one form to another and

relationship among the properties of the system. In steam power plants, gas turbines, cars, motor cycles, scooters etc, heat is converted into work. In

domestic refrigerators, air conditioning plants, cold storage, ice plants and liquefaction plants, work is converted into heat. Solar energy is converted into

heat in solar collectors and into electrical energy in solar cells. Optimal design of thermal power plant or a domestic refrigerator can be obtained by

applying the knowledge of thermodynamics. Even the metabolism of human body can be studied by utilizing the principles of thermodynamics.

The pillars of thermodynamics are its four laws. These are zeroth, first, second and third law of thermodynamics. From zeroth law, temperature is

defined. The first law is essentially the law of conservation of energy and defines energy. 2nd law predicts the direction of heat flow from a higher

temperature to a lower temperature.

1.2 Thermodynamic System, Surroundings, Boundary and Universe

Thermodynamic system is defined as a definite quantity of matter or volume in space upon which attention is focused during a analysis in

thermodynamics. Everything external to a system is called the surroundings. The layer separating the system and the surroundings is called the boundary.

The combination of the system and its surrounding is called the universe.


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Fig. 1.2 Closed system

When the gas is heated, heat Q is supplied to the system and work W is done by gas. In the process piston moves up and boundary rises also. In thediagram, it is observed that heat and work are crossing the boundary but mass of gas is confined within the boundary. Therefore, the system is closed

system. It should be noted that in closed system boundary also moves. To conclude1. A closed system has a fixed mass or quantity of matter.

2. The mass does not cross the boundary of the system.

3. Energy, either in the form of heat or work or both can cross the boundary.

4. Boundary can also move.

1.2.2. Open System

In open system, we pay attention on a specified volume in space. Open system is the system in which both mass and energy cross the boundary.

The popular examples of open system are the air compressor and steam turbine.

Fig. 1.3 displays an air compressor.


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A property is any measurable quantity or characteristics to describe the physical condition of the system. In short, a property is a quantity to

describe the system. These properties may be temperature, pressure, volume, density, internal energy, entropy, enthalpy etc. Thermodynamic properties

are further divided into intensive and extensive types.

1. Intensive propertyIntensive property is the property of a system which is independent of the mass of the system. The examples of intensive property are temperature,

pressure, density, specific volume etc. These are generally denoted by small letters i.e. t, p, , etc.

2. Extensive property

Extensive property is the property of a system which is dependent on the mass of the system. The examples of extensive properties are volume,

mass, kinetic energy, potential energy etc. These are generally denoted by capital letters i.e. V, M,K.E, P.E. etc.

The ratio of extensive property to the mass of the system is known as specific property. Specific property is a intensive property. If we divide

volume, V, by mass, m, we get specific volume. Specific volume is a internal property.

1.3.2 State

State is a condition or position in which a thermodynamic system exists. Condition or position is specified by its properties. At a particular state,

all the properties have fixed values.

(a) Initial state before heating (b) Final state after heating

Fig. 1.4 Initial and final state of a system

Fig. 1.4 shows a gas contained between a cylinder and piston. Before heating at state 1, temperature, pressure, specific volume and internal energy are t1,

p1, v1 and u1. After heating at state 2, temperature, pressure, specific volume and internal energy are t2,p2, v2 and u2. So it can be said that gas can exist in

different states. Thus in present example, change in property, dt,


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2

1

dt dt = t2 t1

It means that t to be property, dt is an exact differential.

1.3.3 Thermodynamic Equilibrium

A system is said to be in thermodynamic equilibrium if the properties of system are same at all the points and do not change with time. The

important properties are temperature, pressure and chemical composition. If the temperature of the system is same at all the points and does change with

time, it is said to be in thermal equilibrium. If pressure of the system is same at all the points and does not change with time, it is said to be in mechanicalequilibrium. If the chemical concentration of the system is same at all the points of the system and does not change with time, if it said to be in chemical

equilibrium.

To attain thermodynamic equilibrium, all the three types of equilibrium, the thermal, the mechanical and the chemical equilibrium must exist.

When system goes from one state to another, and deviation from equilibrium is very small or infinitesimal, it is said to be in quasi-equilibrium.

1.3.4 Process & Cycle

Process is as the path of the successive equilibrium states through which the system passes when it changes its position from state 1 to state 2.

When a system executes one or more processes in such a way that initial and final states of the system are identical, it is said to have executed a cycle.

Fig.1.5 Process and Cycle on p- v diagram

In Fig. 1.5, system undergoes a number of processes and finally returns to initial state 1. 1-2, 2-3, 3-4 and 4-1 are processes and 1-2-3-4-1 is a cycle.

1.4 Work and Heat

1.4.1 Work


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Thermodynamics is a science of transformation of energy from one form to another form. In popular sense energy is the capacity of doing work.

Work is denoted by W. In mechanics, it is defined as the product of force and distance moved in the direction of force. This definition can be used to find

the work to lift a weight, to stretch a spring or a wire. But this definition can not be applied in the study of thermodynamics which deals with system andsurroundings. To calculate work done in thermodynamics, the forces acting on the boundary and its displacement must be known. A broad definition of

work is given in thermodynamics. Work is said to be done by a system on the surroundings if sole effect external to the system could be the raising of a

weight. It can be shown that the definition of work by thermodynamics is more general than given by mechanics.

Fig. 1.6(a) depicts a storage battery as a system with a resistor.

(a) Battery (b) Battery with motor

Fig. 1.6 Flow of current from a battery as work

A current is flowing in the circuit. According to the definition of work as given by mechanics no force is moving any distance. So no work has been done

by the system. But by the definition of thermodynamics, work is being done. In Fig. 1.6(b), if resistor is replaced by a motor having 100% efficiency,

motor can raise the weight and work is done.

In Fig.1.6 (b), if system includes both battery and motor, the work done by this new system on surroundings will be zero.

If work is done by a system, it is considered positive. If work is done on the system, it is taken to be negative. Work is a transient phenomenon. It

only occurs across the boundary when system changes its state. In the definition of work, the weight is not to be actually raised, but it should be possible

to raise the weights by introducing certain changes. In Fig.1.6, resistor was replaced by weight and motor.

1.4.2 Work Done in a Quasistatic Process


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Let us consider a gas contained between cylinder and piston as shown in Fig.1.7(a). Gas is heated, its temperature and pressure increase and piston

is raised up and boundary increased. The process is shown on p-v diagram in Fig. 1.7 (b).

Fig. 1.7 (a) Gas executing a quasistatic process Fig. 1.7 (b) P-V diagram

Fig.1.7 Work done in a quasistatic process

Gas is executing a quasistatic process 1-2. Let p be pressure exerted by gas, dl the distance moved by piston and A area of cross-section of the piston. The

work done by gas when piston moves small distance dl,

W = p Adl = p dv

As piston moves from state 1 to state 2, total work done

W = 2

1

p dv . (1.1)

It is observed in Fig.1.7 (b) that work done during process 1-2 is area under the curve1-2. This area depends on the path 1-2 followed by the gas. If we change the path, area will change, so the work. Therefore, it can be concluded that work

is a path function and does not depend on the states. The work done in different processes is under mentioned.


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1. Work Done in Constant Pressure (Isobaric) Quasistatic Process

Fig. 1.8 Work done in constant pressure process

W12 = 2

1

p dv = p (v2 v1) . (1.2)

2. Work Done in a Constant Volume (Isochoric) Quasistatic Process

Fig. 1.9 Work done in a constant volume process

W12 = 2

1

p dv = 0 (1.3)

3.Work Done in an Isothermal Quasistatic Process


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3. Fig. 1.10 Work done in an isothermal process

W12 = 2

1

p dv

For an isothermal process, pv = C = p1v1 where C is a constant

W12 =

2

1 p dv = v

vp11

2

1 dv

= p1v1v

dv

2

1

= p1 v1 ln1

2

v

v

W12 = p1v1 ln1

2

v

v. (1.4)

4. Work Done in a Polytropic Quasistatic Process


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Fig. 1.11 Work done in a polytropic process

W12 = 2

1

p dv

For a polytropic process,

pvn = p1v1n = p2v2

n = C where n is a index of polytropic process.

Now p =n

n

v

vp11

So W12 = 2

1

dvp =2

1

11 n

n

v

dvvp

W12 =

2

1

1

21

1

v

v

nn

n

vvp

+=

+

= [ ]111

2

11

1

++

nnn

vvn

vp

=n

vvpvvpnnnn

++

1

1

111

1

222

=n

vpvp

1

1122


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W12 =1

2211

n

vpvp..(1.5)

1.4.3 Work Done in Non-equilibrium Process

It was discussed in last article that work done in a quasistatic process or quasi equilibrium is give by the area under p-v diagram or 2

1

dvp .For non-

quasistatic processes, is not given by 2

1

dvp . It will be clear from the examples given below.

1.Work Done by Rotating Paddle on a Gas

Fig.1.12 Non-quasistatic process

Fig.1.12 shows a gas contained in a container work is done by a rotating paddle on the gas. The paddle is rotated by a motor to which electric power is

supplied. The work done on the gas is equal to the power supplied to the motor. In this example work is done on the gas by the paddle but 2

1

dvp is

zero as there is no change in volume of the gas. This is because process is not quasistatic. The paddle is rotating with a high speed so deviation from theequilibrium is not infinitesimal.

2. Work Done against Vacuum


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Fig.1.13. Work done against Vacuum

Fig. 1.13 represents a insulated chamber. Half volume of chamber contains a gas and in other half vacuum exists. Partition is removed and gas occupies

the entire volume. It is observed that now 2

1

dvp is not zero but work done is zero. In this example the process is not quasistatic so expression of work

done equal to 2

1

dvp is not applicable to this system. When partition is removed, gas fills the entire volume rapidly, so change in properties is abrupt

and not the minute as required in quasistatic process. The process is not in equilibrium state. The work done by the gas is zero can be explained in two

ways. From mechanics point of view, work done is zero because vacuum leads to zero or no force, so work done against no force is zero. The

thermodynamically, boundary of the system is changing within the system, volume is doubled, but no work is done on the surroundings outside the system

so, work done is zero.

1.4.4 Heat

Fig. 1.14. Heat transfer between water and a metallic piece

Fig. 1.14. shows a hot metallic piece dropped in a bucket of cold water. It is observed that as time passes, the temperature of metallic piece decreases and

temperature of water

increases till equilibrium temperature is reached. In the process energy is transferred from the hotter body to the cold body. This energy which istransferred by virtue of temperature difference is called heat. Thermodynamically, this energy cannot be called work.

Heat is a form of energy which is transferred from one system to another system or to the surrounding by virtue of temperature difference.


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Like work, heat is transient phenomenon. Heat is never contained by a system. Heat transfer occurs when there is change in temperature within the

system or between the system and the surroundings. If heat is transferred to the system, it is taken to be positive. If heat is transferred from a system to the

surrounding, it is considered to be negative.Like work, heat is a path function. Heat transfer between state 1 and state 2 depends on the path followed between the two states. Heat transfer, Q,

is not a property and not an exact differerential. Therefore, it is denoted by Q and not by dQ. 2

1

Q is denoted by Q12 and not by Q1 Q2.

So to conclude both work and heat are transient phenomena, boundary phenomena and path functions.

td chapter 1

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