thermodynamics introduction

DEFINITIONS

MECH103P – Thermodynamics 2015

Course Structure •  Lectures •  Tutorial sessions •  Laboratory exercises (3) •  Evaluation:

–  Final Exam (1)

•  Resources –  Moodle.ucl.ac.uk –  UCLWiki Thermodynamics page –  Handouts –  Online Discussion Forums –  Surgery Hours

Introduction •  Thermodynamics is the science of the relations between heat,

work and the properties of systems. •  It is the science of energy transfer and its effects on the physical

properties of substances •  It is primarily based upon the observations of common experience

–  formulated into laws, which govern energy conversion. •  The applications of the thermodynamic laws and principles are

found in –  Internal combustion engines –  Gas turbines –  Steam and nuclear power plants –  Air conditioning and refrigeration –  Gas dynamics –  Jet propulsion –  Chemical processing plants –  Any direct energy conversion devices

Thermodynamic System •  In the study of any special branch of physics we usually start with a

separation of a restricted region of space or a finite portion of matter from its surroundings. The portion that is set aside and on which attention is focused is called the system.

•  System is a fixed and identifiable collection of matter enclosed by a real or imaginary surface which is impermeable to matter but which may change its shape or volume. The surface is called the boundary.

•  Surroundings or environment: Everything outside the system which has a direct bearing on the system's behaviour.

Classes of Systems

•  Closed system: –  Fixed mass. No mass transfer across the system boundary;

energy transfer into or out of the system may occur •  Open system:

–  Matter crosses the boundary of the system; energy transfer may also exist

•  Isolated system: –  There is no interaction between the system and the

surrounding

•  Find out about: Control volume, Control surface

•

• • • (1)

(2) •

•

boundary of ??

gas in cylinder

Macroscopic Vs Microscopic •  When a system has been chosen, the next step is to describe it in

terms of quantities related to the behaviour of the system or its interactions with the surrounding or both. Two points of view may be adopted: macroscopic or microscopic

•  Microscopic approach considers the behaviour of every molecule by using statistical methods. The study based on this approach is generally called “Molecular thermodynamics”

•  In Macroscopic approach we are concerned with the gross or average effects of many molecules' interactions. These effects, such as pressure and temperature, can be perceived by our senses and can be measured with instruments. This approach greatly reduces the complexity of the problem and we use this approach in this course. This is known as "Classical Thermodynamics".

Property •  The conditions of the system, and the substance within it, is defined

by the properties of a system. •  A Property is any observable characteristic of a system.

Properties can be defined only when they are uniform throughout a system eg impossible to define the pressure of an exploding system (??).

•  Examples: –  Length, –  volume, –  pressure, –  density, –  refractive index, etc.

Property: Pressure •  A property which is quite important in thermodynamics is the

pressure.

•  A fluid exerts forces on its boundaries, due to the change in momentum of molecules when they collide with the boundary. These forces are not concentrated at one particular point, due to random motion of molecules, but are distributed. Therefore, we can define pressure as the normal force exerted on a surface, divided by the area of the surface.

•  The unit of pressure is the force 1 Newton acting on a square metre area, which is called a Pascal. 1 Pa = 1 N/m2 and 1 bar = 105 Pa

Property: Pressure •  In most thermodynamics investigations we are concerned with the

absolute pressure. However, most pressure gauges measure the difference between the absolute pressure and the atmospheric pressure which is known as gauge pressure.

gauge pressure measured by pressure gauge absolute

pressure

atmospheric pressure

0 pressure

Extensive & Intensive Properties •  In general one can make distinction between two types of

properties. •  (i) Extensive:

–  Extensive properties are those whose value is the sum of the values for each subdivision of the system, eg mass, volume.

•  (ii) Intensive –  Properties are those which have a finite value as the size of the

system approaches zero, eg pressure, temperature, etc. •  Extensive properties may be made intensive by dividing them by

the system mass. For example: system volume = 12 m3, mass = 4 kg system specific volume = 12/4 = m3/kg

State •  The state of a system is fixed by defining all its properties or

sufficient properties so that all others may be described. The state of a system changes if any property changes. In most of the simple systems that we shall consider a small number of properties will be enough to completely define the state of a system.

•  Equilibrium –  A system is in thermodynamic equilibrium if no tendency towards

spontaneous change exists within the system. Energy transfers across the system disturb the equilibrium state of the system but may not shift the system significantly from its equilibrium state if carried out at low rates of change.

•  Note: to define the properties of a system, they have to be uniform throughout the system. Therefore to define the state of a system, the system must be in equilibrium. (Inequilibrium of course implies non-uniformity of one or more properties).

Process (1/2) •  A process is the description of what happens when a system

changes its state by going through a succession of equilibrium states.

•  Property Diagram and Path –  Consider a system which we are monitoring and assume that properties X

(pressure) and Y (eg. volume), which are being measured, are enough to define the state of the system. Then if we plot X versus Y, we get a Property diagram.

x

Y

1

2

Process (2/2) •  A point, such as 1, on the diagram represents the properties of the system at a particular instant and is known as

a state point. Three different hypothetical processes have been drawn: •  Process 1 - 2:

–  is relatively undefined. We cannot guess what happens between the two equilibrium states 1 and 2.

•  Process 3 - 4 –  In this case the properties have been measured at points a, b, c, d, ..., etc, and so we can draw a dotted line

through the points.

•  Process 5 - 6: –  In this case the properties have been measured continuously and we have obtained an infinity of equilibrium

states between 5 and 6. We are now justified in drawing a full line. This line is called the path of the process. Note: to fully define the process we need to monitor the system - surrounding interactions as well.

•  Cyclic Process –  A cyclic process is one for which the initial and final states of the system are

identical.

x

Y

1

2 x

x 3

4

5

6

Interactions Between Systems (Work & Heat) •  What happens when we bring two systems into contact? • 

•  The configuration or states of (A) and (B) may be altered until after a certain time

when the systems reach equilibrium, and there is no change. Systems (A) and (B) can interact even at a distance, eg. earth and moon (tide). But in Thermodynamics, we are concerned with only two kinds of interactions, work and heat.

Thermodynamic Definition of Heat and Work •  In mechanics work is defined as a force acting through a displacement x, the

displacement being in the direction of the force. That is: W = F x x or in the case in which F is varying

•  Unit of work - 1 Nm = 1 Joule •  But this definition of work is very restrictive and not adequate in

Thermodynamics. (Example a system consisting of a battery!)

Work - Interactions Between Systems I •  "Positive work is done by a system,

during a process, when the ONLY effect external to the system could be reduced to the rise of a weight".

•  Definition seems arbitrary! But partly is forced on us since we have to make distinctions between work and heat as a result of the Second Law of Thermodynamics.

•  A simple way to visualise this: –  The system boundary moves in such a way as

to push the lever system to a new dotted position. The work done as in mechanics is (WxL) Nm.

Work - Interactions Between Systems I •  This does not show the width of the application of Thermodynamic

definition. So consider a battery which we take as our system. The battery terminals are connected to a resistor through a switch:

•  When the switch is shut for a time, current flows through the resistor and it becomes "Warmer". Is this a work interaction? Of course from mechanics we would say NO! (since no force has moved its point of

application).

Work - Interactions Between Systems I •  But now let us image that:

•  That is we have imagined a practical arrangement which includes a pulley and an electric motor.

•  If we again close the switch, the electric current will drive the electric motor which winds up a string attached to a weight. That is the sole effect external to the system could be the rise of a weight. This interaction is work!

Some Notes: •  (i) The "ONLY effect", is necessary since, an interaction

in the form of heat transfer could result in the rise of a weight as a part of its effect.

•  (ii) External to the system - Work is defined with respect to a system boundary. If you choose a different system and hence boundary, then work may be changed.

•  (iii) "Could be reduced to" - This means that a weight does not actually have to be raised, but we must be able to visualise a real physical method of raising the weight by hypothetical changes in the surroundings!

•  (iv) "Positive Work"; also implies negative work!

Negative Work •  "If a system does positive work, then obviously the surrounding do an equal amount of

negative work and vice versa. In symbols: W system+ Wsurroundings = 0

•  Sign Convention

Work is done by the system Work is done on the system

•  Important to know: Work is a Transient. It is present during the interaction but does not exist either before or after the interaction. It is something which happens to a system but it is not a characteristic of a system ie not a property!

Further-study •  Homogenous – Heterogeneous systems

•  Types of pressure gauges

•  On Equilibrium State –  Chemical –  Mechanical –  Thermal

•  Quasi-static process

•  Prepare a chart on Units and Dimensions

Interactions Between Systems: Heat and Work

•  Displacement work •  Consider a system consisting of a cylinder and a piston:

•  Assume that the system is in equilibrium, i.e. PA = Force due to weight. Now if we remove the small weight, the finite unbalanced force will cause the system to pass through non-equilibrium states. This is not desired: Thermodynamic state cannot be defined?! So we assume that process is "quasi-static", that is, the force is infinitesimal and so the state is infinitesimally near a thermodynamic equilibrium. This is called fully resisted expansion.

•  But AdL = dV, change in volume of the gas, so:

•  The total work done at the moving boundary can be

performed by integrating this equation, i.e;

•  A number of points should be made here: i) P is the pressure at the systems' boundary and not necessarily the system pressure! ii) dV is the differential of the volume swept out by the system boundary and not in general the differential of the system volume e.g. à iii) The total work done by a system is not equal to integral of pdV since other forms of work such as electrical, magnetic etc might be present!

Interactions Between Systems: Heat and Work

The relationship between P&V •  At the start of the process, the piston is at position 1, the

pressure being relatively low. At the end of the process the piston is at 2. Assume the process is quasi-static so that we know the state of the system from 1-2 and so can draw a full line. The work done on the air during the compression process = = Area under the curve 1-2, or (1-2-b-a)

•  Possible to go from 1 to 2 along many different quasi-static paths, such as B & C. Since the work done is equal to the area underneath the curve, we can see that the amount of involved in each case is a fraction not only of the end-states of the process, but in addition is dependant on the path that is followed in going from 1-2. For this reason work is called a path function, as opposed to thermodynamics properties which are point functions.

Special cases of P&V relationships

1.The constant volume process (isochoric)

Area underneath curve = 0


2. Constant pressure process (isobaric)


3. PV= constant process This simple algebraic formula is in fact satisfied by many substances when expanding in fully resisted expansion at constant temperature, so called isothermal process.


4. PVn= k (constant) Also known as the polytropic process. This represents a family of processes which are very useful approximations to real processes.

Un-resisted expansion Consider a rigid vessel divided by a light diaphragm: When diaphragm gives way under pressure the gas expands to fill the whole vessel. If we consider system S1

:

The pressure on the moving boundary, i.e. The face of the boundary exposed to vacuum is always zero while that part of the boundary is in motion. Consider S

2: Initial 0, finally volume is the same, so W = 0

P=1atm P=0

S1 S2

diaphragm

dv=0

Shear work Consider a block being pushed along a rough horizontal surface by an agent which applies a force F. Assume that we want to calculate the work done on the lower part of the block by the system consisting of the agent and the upper part of the block. A shear exists along the part of S in the block tending to make the upper half of the block slide relative to the lower half. If this shear stress has uniform value and acts over area A, then from static: Thus or in general:

I.e. when sigma is a function of (L), we consider each element of area dA separately and multiply by the value of sigma prevailing there at the moment in question and by the elementary distance dL.

Shaft work A very important form of shear work which we are concerned with is shaft work. This comes across in actions such as power transmission in cars and steam turbines, gas turbines etc. Consider a shaft penetrating a system boundary: Where the shaft crosses the boundary S, for each element of cross-section area dA there is a shear stress sigma in the tangential direction, tending to cause the relative rotation of the two parts of the shaft on either side of S i.e. the torque dT on the element =

Suppose that shaft turns through a small angle and as a result each element (both sides of S) moves a distance in the direction of the stress. The shear work done by the element dA on its surroundings during the elementary rotation is given by: Thus the shear work done by the system on the surroundings is given by: or For steady condition T is constant and independent of , then: Dividing both sides by dT (time increment), we obtain the shaft power, Where

∫=∴

=

rdATdArdTσ

σ

θ

))(( θσ rddAdWs =

Electrical work In an electric field, electrons in a wire move under the effect of electromotive forces, doing work. When N electrons move through a potential difference V, the electrical work done is: We = VN(kJ) Which can be expressed in the rate form as: Where

Interaction Between Systems II - Heat The thermodynamic definition of heat is: "Heat transfer is the interaction between systems which occurs by virtue of their temperature difference when they communicate". But what is temperature? Temperature is the thermodynamics property that we are most familiar with and yet it is amongst the most difficult properties to define! On the microscopic level temperature is related to the kinetic energy of the molecules. But in thermodynamics we are interested in temperature because it enables us to know whether or not two system are in thermal equilibrium. So we define temperature as:"The temperature of a system is a property that determines whether or not a system is in thermal equilibrium with other systems".

Interaction Between Systems II - Heat The concept of thermal equilibrium is very familiar to us: Cold bottle of milk from fridge and cup of hot water, if left in a room for few hours… will reach the same temperature as that of the room.. That is they both reach thermal equilibrium with the room. Thus we say: "Two systems are equal in temperature if no change in any property occurs when they are bought into communication". We can also conclude that: "Two systems which are equal in temperature to a third system are equal in temperature to each other". This is the Zeroth Law of Thermodynamics and provides the basis for temperature measurements.

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Temperature inequality & thermometers Consider an experiment involving three systems S1, S-2 and S3. Suppose we bring S3 into contact with S1 until they reach thermal equilibrium. No work interactions assumed! Now if we bring S3 into contact with S2 and as a result observable changes occur in S3¸ then we can conclude that the temperatures of S1 and S2 are unequal. To measure this inequality we use a thermometer.

Thermometers For thermometer, we can use any property that changes with temperature. For example, if we chose a glass tube containing mercury as system S3, then we would have a mercury in glass thermometer. The mercury in glass thermometer is usually calibrated between two fixed points- one at the melting point of ice and the other at the boiling point of water- both at the pressure of one atmosphere. Temperature scales are then defined by assigning numbers to the ice point and steam point and to the equally-spaced points between them. Celsius or centigrade: Ice point: 0 deg C. Steam point: 100 deg C, with 100 equal subdivisions. Farenheit: Ice point: 32 deg F. Steam point: 212 deg F, with 180 equal subdivisions. Other thermometers: 1. Constant volume thermometer, gives a very close result to the thermodynamic temperature scale which is not based on a particular thermometric substance. 2. Platinum resistance thermometer


Sign Conventions for Heat transfer

Heat transfer is +ve when the surroundings have a higher temperature i.e. heat is transferred to the system Heat transfer is -ve when the system has a higher temperature, i.e. heat is transferred from the system Heat like work is transitory, i.e. not an observable characteristic of the system. Of course it is a path function.


Some Notes on Definition of Heat 1.  Heat is not "that which inevitably causes a temperature rise".

For example if a system comprising of ice and water is heated, no temperature rise occurs at least until the ice has melted.

2. Heat is not "that which is always present when a temperature rise happens". E.g.

from below, water can be heated by work only.

How heat transfer occurs

Conduction: Conduction is a mode of heat transfer involving solid media due to the impact of adjacent molecules vibrating about mean position. Some solids such as metal rods, copper and silver are very good conductors, while others like wood, cork are very poor conductors and are used as insulators. Convection: This is a mode of heat transfer in a fluid media in motion, e.g. hot wall heats a mass of air which moves to heat a cold wall Radiation: Thermal communication which involves no matter of media, e.g. sun radiates heat to warm the earth. The rate of radiative heat transfer increases rapidly with temperature but is negligible at room temperature. Adiabatic processes: If all the above three modes of heat transfer are absent then Q=0, and we have an adiabatic process.

Thermometers For thermometer, we can use any property that changes with temperature. For example, if we chose a glass tube containing mercury as system S3, then we would have a mercury in glass thermometer. The mercury in glass thermometer is usually calibrated between two fixed points- one at the melting point of ice and the other at the boiling point of water- both at the pressure of one atmosphere. Temperature scales are then defined by assigning numbers to the ice point and steam point and to the equally-spaced points between them. Celsius or centigrade: Ice point: 0 deg C. Steam point: 100 deg C, with 100 equal subdivisions. Farenheit: Ice point: 32 deg F. Steam point: 212 deg F, with 180 equal subdivisions. Other thermometers: 1. Constant volume thermometer, gives a very close result to the thermodynamic temperature scale which is not based on a particular thermometric substance. 2. Platinum resistance thermometer


First law of thermodynamics One important concept in thermodynamics is the relationship between heat and work. However, there is no logical relationship between heat and work and so it had to be found experimentally. The experiments were carried out by J P Joule between 1840 to 1849. The important experiment involved a system consisting of a well-lagged cylinder containing water going through a cycle composed of two processes. In the first process, shear work was done on the system when a paddle turned as a weight was lowered, as shown here. As a result of this process the water temperature was found to rise steadily. When the temperature reached a certain value, the paddle wheel was stopped and the work done noted (historically in foot pounds-force). In the second process the system was brought into contact with a cold body so that heat was transferred from the system, as shown here.

First law of thermodynamics

This process was then cut-off when the system reached its original state and again the amount of heat transfer was noted down (in British Thermal units or calorie). After making the measurements for a variety of systems and for various amounts of work and heat, it was found that the amounts of work and heat were always proportional. These observations were then formalised into the First Law of Thermodynamics which is stated as: "If any system is carried through a cycle (the end state being precisely the same as the initial state) then the net work is proportional to the net heat transfer".

Where J is a constant known as the Mechanical Equivalent of Heat. In British units J is 778 ft lbf per Btu and in SI units its 1. Nm per Joules

∫ ∫= dQJdw or ∫ ∫= dQdw In SI units


First law for non-cyclic process We defined first law for cyclic processes, but what happens when we have a change of state. For this purpose consider a system that undergoes a cycle changing from state 1 to 2 by process A and returning from state 2 to 1 by process B, as shown in the image:

Subtracting the equations we get: or on rearranging:

Now consider another cycle, the system changing from State 1 to 2 by process A and returning to state 1 by process C, so that


Energy.. Since B & C represent arbitrary processes between states 1 and 2, we can conclude that the quantity (dQ -dW) is the same for all processes between states 1 and 2. Therefore, (dQ -dW) depends only on the initial and final states and not on the path followed between the two states. That is this quantity is a point function, which means that it is a property of the system, called the energy of the system and is given smybol E-

When we integrate this equation we get: where: 1Q2 is the heat transferred to the system during process 1 - 2 E2 and E1 are the energy at the initial and final states 1W2 is the work done during process 1 - 2 E represents all the energy in the system i.e. E = P. E + K.E. + energy associated with position and motion of molecules + chemical energy (e.g. storage battery), etc. In thermodynamics it is convenient to consider the bulk K. E. and P.E. separately and then to consider all the other energy of the system in a single property that we call internal energy, U.

So: E = U + KE + PE dQ = dU + d (KE) + d(PE) + dW


Expression for KE Consider a system initially at rest acted on by a horizontal force F that moves the system a distance dx in the direction of the force. dW = - Fdx = - d KE


Expression for PE Consider a system initially at rest. Let this system be acted on by a vertical force F that is of such magnitude that it raises (in elevation) the system with constant velocity an amount dz. If acceleration due to gravity is g

dW = - F d Z = - dPE But: F = Ma = mg Then: dPE = FdZ = mgdZ

Thus we can write:

Observations..

We can make three observations about this equation. (i ) We can write the first law of Thermodynamics for a system which changes its state during a non-cyclic process, when we employ the property of system E energy. (ii) The net change of the energy of the system is always equal to the net transfer of energy across the system boundary as heat and work. This is somewhat similar to a husband and wife having a joint bank account. There are two ways in which deposits and withdrawals can be made, either by husband or wife, and the balance will always reflect the net amount of the transaction - Similarly there are two ways in which energy can cross the boundary of a system, either as heat or work, and the energy of the system will change by the exact amount of net energy crossing the system boundary. This leads to the law of conservation of energy: "The energy of a system remains unchanged if the system is isolated from its environment as regards to work and heat regardless of the nature of changes within the system". (iii) Equations (1) can give only changes in, internal energy, PE and KE. We can learn nothing about absolute values of these quantities. Therefore, we must assign reference states to these quantities. Easy to assign reference states for PE, e.g. zero elevation on surface earth and KE, zero KE when velocity is zero relative to earth but more difficult for U. (iv) This equation also implies that "a perpetual motion machine of a first kind is impossible" This device is a system which will continuously deliver work without a supply of heat i.e. Q = 0, W =+ ve, dU –ve. Thus work is obtained at the expense of internal energy which will eventually run out. (v) Internal energy is an extensive property. But of course u=U/m, is an intensive property. (vi) dU is an exact differential?

to continue…

thermodynamics introduction

Documents

isolated system

open system

exploding system

system energy transfer

macroscopic approach

science of energy transfer

molecular thermodynamics

classical thermodynamics