Elements of Mechanical Engineering�(Thermodynamics)�

By

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M K Sindhu

Course Objectives

• Student should able to understand Basics of Mechanical Engineering
• Student should able to understand laws of thermodynamics
• Student should able to understand Energy Equations and applications.
• Student should able to access properties and tables.
• Student should able to understand Process.
• Student should able to understand entropy & its application.
• Student should able to understand power transmission devices.

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Course Outcomes

Thermodynamics

• The name thermodynamics stems from the Greek words therme (heat) and dynamis (motion).
• Thermodynamics is the science of energy conversion involving heat and other forms of energy, most notably mechanical work.
• Thermodynamics is the study
• system & surrounding
• Energy & its transformation
• Relationship between heat & work
• Properties of working fluid
• 3 E’S ENERGY ENTROPY EQUILIBRIUM

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Why we study Thermodynamics ?

• We study thermodynamics because the principle and concepts are found in everywhere in our day-today life. Such as
• Power producing devices
• Power consuming devices
• Chemical & industrial processes
• Secondly thermodynamic is the important tool for innovation, design & development of new machines

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Applications of thermodynamics

THERMODYNAMICS AND ENERGY

• Thermodynamics: The science of energy.
• Energy: The ability to cause changes.
• Conservation of energy principle: During an interaction, energy can change from one form to another but the total amount of energy remains constant.
• Energy cannot be created or destroyed
• Stored energy Transit energy

Energy stored within energy

System boundary crosses

boundary

Branches of Thermodynamics

• Classical thermodynamics /Macroscopic
• Macro means big total or overall(study is made by several molecules)
• Structure of matter is not considered.
• No attention is focused on behavior of each particle.
• Volume is assumed to be vary large compare to molecule

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• Statistical thermodynamics/Microscopic
• Micro means small(study is made by each molecule)
• Structure of matter is considered.
• attention is focused on behavior of each particle.
• Complex & time taking.

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Equilibrium and non-equilibrium thermodynamics

• The word equilibrium implies a state of balance. In an equilibrium state there are no unbalanced potentials, or driving forces, within the system.
• Equilibrium thermodynamics is the systematic study of transformations of matter and energy in systems as they approach equilibrium.
• A system is said to be equilibrium if it does not undergo any further change of its state

Equilibrium classification

• Mechanical : equality of force and pressure
• Thermal: equality of temp.
• Chemical :equality of chemical potential
• Thermodynamic: all of these above

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A system reaching thermal equilibrium

Thermodynamic system.

A thermodynamic system (a physical system) is a precisely defined macroscopic region of the universe that is studied.

A thermodynamic system is defined as a space or region upon which our aim is focused.

Everything external to a system is known as surrounding & the system is separated from surrounding by boundaries

Thermodynamic systems

• Closed systems are able to exchange energy (heat and work) but not matter with their environment.
• Energy cross but mass can’t.
• Ex: piston fitted with a cylinder providing heat piston moves upward ie transformation of heat energy but mass remains constant.

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Thermodynamic systems

• Open systems may exchange any form of energy as well as matter with their environment
• Both mass & energy crosses system boundary
• Ex: water heater, boiler, compressor ,turbine

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Thermodynamic systems

• Isolated systems are completely isolated from their environment. They do not exchange heat, work or matter with their environment. An example of an isolated system is a completely insulated rigid container, such as a completely insulated gas cylinder. M= Constant, E=Constant

PROPERTIES OF A SYSTEM

• Property: Any characteristic of a system.
• Some familiar properties are pressure P, temperature T, volume V, and mass m.
• Properties are considered to be either intensive or extensive.
• Intensive properties: Those that are independent of the mass of a system, such as temperature, pressure, and density.

P=P₁

• Extensive properties: Those whose values depend on the size—or extent—of the system.

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Criterion to differentiate intensive and extensive properties.

Internal energy

• Internal energy is defined as the energy associated with the random, disordered motion of molecules.
• It is separated in scale from the macroscopic ordered energy associated with moving objects; it refers to the invisible microscopic energy on the atomic and molecular scale.
• The internal energy is the total energy contained in a thermodynamic system. It is the energy necessary to create the system, but excludes the energy associated with a move as a whole, or due to external force fields. Internal energy has two major components, kinetic energy and potential energy.
• For an ideal monoatomic gas, this is just the translational kinetic energy of the linear motion of the "hard sphere" type atoms. However, for polyatomic gases there is rotational and vibrational kinetic energy as well.

System Work

• When work is done by a thermodynamic system, it is ususlly a gas that is doing the work. The work done by a gas at constant pressure is:

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• For non-constant pressure, the work can be visualized as the area under the pressure-volume curve which represents the process taking place. The more general expression for work done is:

Heat Transfer

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Heat is energy transferred from one body or thermodynamic system to another due to thermal contact when the systems are at different temperatures.

Heat Conduction

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Heat Conduction

Conduction is heat transfer by means of molecular agitation within a material without any motion of the material as a whole. For heat transfer between two plane surfaces, such as heat loss through the wall of a house, the rate of conduction heat transfer is:

Heat Transfer

Heat Convection

• Convection is heat transfer by mass motion of a fluid such as air or water when the heated fluid is caused to move away from the source of heat, carrying energy with it.

Heat Transfer

Heat Radiation

• Radiation is heat transfer by the emission of electromagnetic waves which carry energy away from the emitting object. For ordinary temperatures (less than red hot"), the radiation is in the infrared region of the electromagnetic spectrum. The relationship governing radiation from hot objects is called the Stefan-Boltzmann law:

where P is net radiated power, heat Q transferred in unit time t,

σ – Stefan’s constant, σ=5.6703x10-8 Watt/m2 k4

S – radiating area,

T_r – absolute temperature of radiator,

T_s – absolute temperature of surroundings,

e - emissivity (=1 for ideal radiator – black body)

Heat Transfer

Heat Transfer by Vaporization

• If part of a liquid evaporates, it cools the liquid remaining behind because it must extract the necessary heat of vaporization from that liquid in order to make the phase change to the gaseous state. It is therefore an important means of heat transfer in certain circumstances, such as the cooling of the human body when it is subjected to ambient temperatures above the normal body temperature.

where m is mass of liquid

L - heat of vaporization at liquid boiling point

Zeroth law of thermodynamics

• The first law of thermodynamics is the application of the conservation of energy principle to heat and thermodynamic processes:

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Heat added to the thermodynamic system goes to change the internal energy and to do the work by the system.

First law of thermodynamics

• The first law of thermodynamics is the application of the conservation of energy principle to heat and thermodynamic processes:

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Heat added to the thermodynamic system goes to change the internal energy and to do the work by the system.

First law of thermodynamics

The internal energy of a system can be changed by heating the system or by doing work on it.

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• If the system is isolated, its internal energy cannot change.

Heat Engine

• A heat engine is a system that performs the conversion of heat to mechanical work. A heat "source" generates thermal energy that brings the working substance to the high temperature state. The working substance generates work in the "working body" of the engine while transferring heat to the cold reservoir until it reaches a low temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid.

Heat Engine

• Q_in is the heat flow from the hot reservoir to the engine
• Q_out is the heat flow from the engine to the cold reservoir.
• The work done by the heat engine is the difference between Q_in and Q_out.
• Heat engine efficiency:

Entropy as a Measure of the Multiplicity of a System

The probability of finding a system in a given state depends upon the multiplicity of that state. That is to say, it is proportional to the number of ways you can produce that state. Here a "state" is defined by some measurable property which would allow you to distinguish it from other states. Entropy:

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where k is Boltzmann's constant, W is the number of microstates The k is included as part of the historical definition of entropy and gives the units J/K in the SI system of units. The logarithm is used to make the defined entropy of reasonable size. The multiplicity for ordinary collections of matter are on the order of Avogadro's number, so using the logarithm of the multiplicity is convenient.

Entropy in Terms of Heat and Temperature

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• A the change in entropy can be described as the heat added per unit temperature

ΔS = Q/T

where S is the change in entropy,

Q is the heat flow into or out of a system, and T is the absolute temperature in degrees Kelvin (K).

• This is often a sufficient definition of entropy if you don't need to know about the microscopic details. It can be integrated to calculate the change in entropy during a part of an engine cycle.
• The concept of entropy (S) gives us a more quantitative way to describe the tendency for energy to flow in a particular direction.

Entropy

Thermodynamic Potentials

• Four quantities called "thermodynamic potentials" are useful in the chemical thermodynamics of reactions and non-cyclic processes. They are internal energy, the enthalpy, the Helmholtz free energy and the Gibbs free energy. The four thermodynamic potentials are related by offsets of the "energy from the environment" term TS and the "expansion work" term PV. A mnemonic diagram help you keep track of the relationships between the four thermodynamic potentials.

Enthalpy

• Enthalpy is a thermodynamic potential. It is a state function since it is defined in terms of three other precisely definable state variables, and it is an extensive quantity. Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy U, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume V and pressure P.

H = U + PV

• It is somewhat parallel to the first law of thermodynamics for a constant pressure system

Q = ΔU + PΔV, since in this case Q=ΔH

Thermodynamic free energy

• The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to perform work. This unusable energy is given by the entropy of a system multiplied by the temperature of the system. Free energy is that portion of any first-law energy that is available to perform thermodynamic work; i.e., work mediated by thermal energy. Free energy is subject to irreversible loss in the course of such work. Since a first-law energy is always conserved, it is evident that free energy is an expendable, second-law kind of energy that can perform work within finite amounts of time. Several free energy functions may be formulated based on system criteria.

Free energy functions

• The historically earlier Helmholtz free energy is defined as

• Its change is equal to the amount of reversible work done on, or obtainable from, a system at constant T. It is "work content“. Since it makes no reference to any quantities involved in work (such as p and V), the Helmholtz function is completely general: its decrease is the maximum amount of work which can be done by a system, and it can increase at most by the amount of work done on a system.

Free energy functions

• The Gibbs free energy

The internal energy U might be thought of as the energy required to create a system in the absence of changes in temperature or volume. But as discussed in defining enthalpy, an additional amount of work PV must be done if the system is created from a very small volume in order to "create room" for the system. As discussed in defining the Helmholtz free energy, an environment at constant temperature T will contribute an amount TS to the system, reducing the overall investment necessary for creating the system. This net energy contribution for a system created in environment temperature T from a negligible initial volume is the Gibbs free energy.

Free energy functions

• Historically, these energy terms have been used inconsistently. In physics, free energy most often refers to the Helmholtz free energy, while in chemistry, free energy most often refers to the Gibbs free energy.
• For processes involving a system at constant pressure p and temperature T, the Gibbs free energy is the most useful because, in addition to subsuming any entropy change due merely to heat, it does the same for the pdV work needed to "make space for additional molecules" produced by various processes. (Hence its utility to solution-phase chemists, including biochemists.) The Helmholtz free energy has a special theoretical importance since it is proportional to the logarithm of the partition function for the canonical ensemble in statistical mechanics. (Hence its utility to physicists; and to gas-phase chemists and engineers, who do not want to ignore pdV work.)

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The second law of thermodynamics�Clausius statement

• The second law of thermodynamics describes the flow of energy in nature in processes which are irreversible.
• The second law of thermodynamics may be expressed in many specific ways.

Second Law and Refrigerator

• It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. Energy will not flow spontaneously from a low temperature object to a higher temperature object.
• This precludes a perfect refrigerator.
• The statements about refrigerators apply to air conditioners and heat pumps, which embody the same principles.

Kelvin-Planck statement

Second Law and Heat Engine

• It is impossible to extract an amount of heat from a hot reservoir and use it all to do work. Some amount of heat must be exhausted to a cold reservoir.
• It meams that the efficiency of a heat engine cycle is never 100%.
• This precludes a perfect heat engine.

Second Law and Entropy

• The second law of thermodynamics is closely related to the concept of entropy, or the disorder created during a thermodynamic process.
• In any cyclic process the entropy will either increase or remain the same.
• Since entropy gives information about the evolution of an isolated system with time, it is said to give us the direction of "time's arrow“.

Other Second Law Formulations

• In practical applications, this law means that:
• Any heat engine or similar device based upon the principles of thermodynamics cannot, even in theory, be 100% efficient.

Equivalence of the statements

Kelvin Statement from Clausius Statement

Suppose there is an engine violating the Kelvin statement: i.e.,one that drains heat and converts it completely into work in a cyclic fashion without any other result. Now pair it with a reversed Carnot engine as shown by the graph. The net and sole effect of this newly created engine consisting of the two engines mentioned is transferring heat from the cooler reservoir to the hotter one, which violates the Clausius statement. Thus a violation of the Kelvin statement implies a violation of the Clausius statement, i.e. the Clausius statement implies the Kelvin statement. We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and hence the two are equivalent.