Temperature and heat

Thermal equilibrium:

By touch we can distinguish between a hot body and a cold body. If a hot system is brought into contact with a cold system , both systems will under go changes. The degrees of hotness and coldness of the respective systems will change , and finally a stage will be reached when the hotness (or coldness) of the two bodies does not change anymore. Then the two bodies can be said to be in thermal equilibrium.

The Zeroth law of Thermodynamics:

The Zeroth law state that if two systems taken separately can each be in equilibrium with a third system , the two can be at equilibrium with each other. Thus any two systems which are in thermal equilibrium have a property in common : this property can be defined as temperature. 

Heat: 

When two systems having different temperatures are in contact , the change toward equilibrium are brought about by an interaction across the boundaries which are in contact. The interaction which has taken place in this instance is called a heat interaction. Heat and work are both boundary interactions , and any interaction which cannot be classed as a heat interaction is a work interaction. 

Measurement of heat:

Heat was once measured using a set of units different from that for work. In the British Systems of units it was measured in terms of the Btu( British thermal unit ) which is the heat necessary to increase the temperature of 1 pound of water by 1°F and in the CGS system the unit is the calorie which is the heat necessary to increase the temperature of 1 gram of water by 1°C . In the SI , both heat and work are measured in joules(J).

Work Transfer

preamble:

In mechanics , work is defined as the scalar product of the force vector and the displacement vector of its point of application. As we develop the subject of thermodynamics we will find that this definition of work is inadequate , that is , it fails to cover many other types work interaction which are fully convertible to one another and to mechanical work. Thus a thermodynamic system can do work without exerting a ' mechanical ' force which moves a point of application.

The thermodynamic definition of work:

An interaction between a system and the surroundings is a work interaction if , during a given process , if the only effect outside the system could be reduced to one of the raising(or the lowering) of a weight. 

To show that a system does work during a given process , we replace the normal environment of the system by a device which can interact with the system during an identical internal process , and raise(or lower) a weight as the one and only result of the interaction. 

Work during boundary expansion:

If a system which is in internal equilibrium expands slowly , the rate of expansion being such that the increase in kinetic energy of the system or any part of the surroundings is negligible , the work transfer from the system to surroundings for an element increase(δV) of the volume is given by ;

-δW = p δV

where the p is the pressure of the system at the instant when the volume is V. Work is written with a negative sign because the notation that work done on the system is positive. The above expression also be written as ;

-dW = p dV

The total work during any finite process 1-2 can be found by integration of the above expression. 

Other types of work:

Besides systems which under go a volumetric expansion , there are others which may be of engineering interest. In all these ;

dW = force(F) . displacement(dX) 

Here the concept of force has been generalized to include the appropriate intensive properties , and the displacements(X) are conjugate extensive properties the change of which constitute displacements associated with the 'force' F. 

Units and dimensions

Introductory remark:

Any physical quantity has a twofold value. It has one component with a dimensional significance and another with a numerical significance. Both components are equally important , and should be specified together. 

Mathematical manipulation of numbers leads to quantitative answers to problems of engineering interest. For these answers to be correctly interpreted without difficulty by all concerned it is essential to have a system of units which is adhered to by all. 

Dimensions:

Five fundamental dimensions , namely ;

• Mass(M)  
• Length(L) 
• Time(T) 
• Quantity of heat interaction(H) 
• Temperature(Θ)     

were used in classical thermodynamics. The dimensions of all other thermodynamic quantities were expressed in terms of these five.   

Systems of units:

Out of the many systems of the units available to us , two deserve special mention :

• The British (or imperial) system
• The international (SI) system 

The British System has four basic mechanical units , namely ;

• Pound (mass)   'lb'
• Foot (length)   'ft'
• Second (time)   's'
• Pound-Force (force)   'lbf'

One pound-force is the force necessary to give one pound of matter and acceleration of 32.174 ft/s². Familiarity with this system is still important because of its continued use in a few industrialized countries , especially the USA.

Pressure:

In engineering practice pressures are measured by instruments such as manometers , Bounder pressure gauges and pressure transducers which give an indication of the difference between the measured pressure and the atmospheric pressure. The pressure reading given by the instrument is called the gauge pressure , so that ;

Absolute pressure(p) = Gauge pressure(p_g) + Atmospheric pressure(p_a)

Absolute pressures which are less than atmospheric are specified in terms of vacuum , which is defined by ;

Vacuum(p_v) = Atmospheric pressure(p_a) - Absolute pressure(p)

When giving the values of pressures it is extremely important to specify whether they are absolute values(by writing abs after the number and unit) or gauge values or a vacuum (by writing either gauge or vac after the unit). Where the nature of the quantity is not specified , it may be assumed to be the gauge or the absolute value , depending on what the reader is used to. Where a large number of pressure values need to be given , it is convenient to declare at the beginning that all values are absolute(or gauge). 

Introduction

Thermodynamics is the science of the relationship between heat , work and the properties of the systems. More recently Thermodynamics has been defined as the science of energy and its relation to matter. Thermodynamics is based on the laws of Thermodynamics referred to as the ,

• Zeroth law
• First law
• Second law 
• Third law

These laws result from our experiences of the world of inanimate matter. They are accepted as laws of of nature because they have not been violated even in single instance. Based on these laws , methods of Thermodynamic analysis have been built up by the use of logic and mathematics.

By means of these methods we are able to predict the behavior of Engines , Refrigerators , and other fluid handling machinery , and of matter subjected to chemical reactions , electrical and magnetic processes or other transactions which affect energy.

Thermodynamic systems

matter:

The physical world is made of matter. If we take what is called a microscopic view , we find that matter is made up of atoms or , in many cases , identifiable groups of atoms , which are called molecules. A subdivision of matter into smaller and smaller parts brings us progressively to , molecules and atoms ; protons , neutrons and electrons.

The energy possessed by a given piece of matter can in the final analysis be associated with its micro structure , i.e. the arrangement of and the inter-relationships between the subdivisions of matter. For example , a mass of gas will have energy by way of the Kinetic energy of molecules which are in random motion. The stretching of a rubber band causes the long-chain molecules which are random motion.  The stretching of a rubber band causes the long-chain molecules in it to change their shape; this strains the bonds between atoms which form the molecules. Here we find storage in the form of Strain energy. The linkage of atoms in a molecule or in a crystal brings about the straining of valency bonds , and this is the manner in which Chemical energy is stored. The electrons which go around the nucleus of an atom have energy by virtue of their linear velocity and of spin about their own axes. The nucleus can spin about its axis and thus have Rotational kinetic energy. Within the nucleus the protons and neutrons being held close to each other results in the storage of energy. This is called Binding energy. Relativistic  mechanics tells us that matter and energy are interchangeable. Even though matter and energy are associated with each other in a discrete manner on a microscopic level , the subject of thermodynamics deals with matter in the form of continuum. In order to see matter as a continuum , we take what is called a macroscopic view. A macroscopic view does not get us involved with the velocities and energies of individual particles ; we can describe matter in terms of statistically derived quantities which cannot be associated with single particles , but are meaningful only in relation to groups.

System: 

A thermodynamic system consists of matter which we can identify. Identification requires that the matter , irrespective of the phase or mixture of phases obtaining in it , remains within an identifiable  and continuous boundary. The System boundary  will enclose all the matter associated with the system and leave out all that which is not a part of the system. This boundary may be real or imaginary , and all matter outside boundary forms the surroundings or the environment.

Closed system:

A system is referred to as an open system when no matter crosses its boundary. Thus the matter enclosed by the system boundary remains the same throughout.

Open system: 

If matter flow pass the boundary , the system is referred to as an Open system. Here we are able to identify the matter entering and leaving the system during any period and also the matter present within the boundary at any time. there may be more than one incoming stream and more than one out going stream through which matter enters and leaves. The streams may be steady or non-steady.

In thermodynamics and fluid mechanics , the system boundary , especially that of an open system , is also referred to as the control surface. The enclosed space is referred to as the control volume , we can write the continuity equation.

Property:

To have a complete knowledge of a system at a given instant in a thermodynamic sense we must know its  properties. Each property can be assigned a numerical value. The values of the properties will not tell us anything about the history of the system. Volume , mass , pressure , temperature , energy , magnetization , and polarization , are of some of the properties which may be interest to us. Particularly , volume , temperature , and pressure are properties which only thermodynamics systems can have ; individual atoms, molecules and sub-atomic particles do not have these properties. 

We can classify properties into two groups ,

• Intensive
• Extensive

 Intensive properties can be defined at a point or locality within a system , and extensive properties refer to the system as a whole so that they depend on the extent of the system.   

State of a system:            

The state of a system is fixed by all of its properties. 

state = f ( all properties)

The thermodynamic ' state ' must not be confused with the ' phase ' of a substance.

Internal equilibrium:

If there are no local variations of properties within a closed system at a given instance , then we say that it is in internal equilibrium. If the closed system is kept in isolation for a sufficiently long time , local variations in its properties can be made as small as we like.( When a closed system is isolated in such a way that the surroundings cannot influence it at all , it is said to be isolated.)

Process:

A process is an action that makes a system change from one state to another. the cyclic process is a special kind of process is in which the starting and the finishing states are identical.