Quantities and Units: SI System

Quantities and Units

• SI Units (Systéme International) are utilized
• The primary quantity name Length has the symbol of 1 and the corresponding SI Unit/Symbol is Meter/m
• The primary quantity name Mass has the symbol of M and the corresponding SI Unit/Symbol is Kilogram/kg
• The primary quantity name Time has the symbol of t and the corresponding SI Unit/Symbol is Second/s
• The primary quantity name Electric current has the symbol of I and the corresponding SI Unit/Symbol is Ampere/A
• The primary quantity name Thermodynamic temperature has the symbol of T and the corresponding SI Unit/Symbol is Kelvin/K
• The primary quantity name Amount of substance has the symbol of n and the corresponding SI Unit/Symbol is Mole/mol
• The primary quantity name Luminous intensity has the symbol of Iv and the corresponding SI Unit/Symbol is Candela/cd
• *Note the symbol υ is not a listed primary quantity with a corresponding value listed
• The derived quantity name Force has the corresponding SI Unit/Symbol is Newton/N (m kg-2)
• The derived quantity name Pressure (or stress) has the corresponding SI Unit/Symbol is Pascal/Pa (N m-2)
• The derived quantity name Energy (or work or quantity of heat) has the corresponding SI Unit/Symbol is Joule/J (N·m)
• The derived quantity name Surface tension has the corresponding SI Unit/Symbol is Newton per meter/Nm-1
• The derived quantity name Heat capacity (or entropy) has the corresponding SI Unit/Symbol is Joule per kelvin/JK-1
• The derived quantity name Specific heat capacity, and specific entropy has the corresponding SI Unit/Symbol is Joule per kilogram kelvin/J kg-1 K-1
• The derived quantity name Specific energy has the corresponding SI Unit/Symbol is Joule per kilogram/J kg-1
• The derived quantity name Molar energy has the corresponding SI Unit/Symbol is Joule per mole/J mol-1
• The derived quantity name Molar heat capacity (or entropy) has the corresponding SI Unit/Symbol is Joule per mole kelvin/J mol-1 K-1
• Symbols in parentheses refer to primary units

Why study Thermodynamic in Materials Science ?

• Thermodynamics the basis for understanding how materials respond to changes in temperature, pressure, and composition
• The critical link between processing microstructure requires a knowledge of the relevant thermodynamics principles.
• Thermodynamics enables maps of equilibrium states for broad spectrums of systems and influences
• Such maps are used in science and industry to answer real-world questions about behavior of matter
• Examples of real-world questions about the behavior of matter
  • Will cadmium melt at 545°C?
  • If the temperature of the air outside drops eight more degrees, will it get foggy?
  • If I heat this Nb–Ti–Al alloy in air to 1100°C, will it oxidize?
  • Can this polymer solvent dissolve 25% PMMA at room temperature without phase separating?
  • How can I prevent the oxidation of silicon carbide when I hot press it at 1350°C?
  • How can I control the defect concentration in this fuel cell membrane?
  • What source temperatures should I use to codeposit a 40 to 60 Ge–Si thin film from the vapor phase?
  • Will silicon carbide fibers be stable in an aluminum nitride matrix at 1300°C?
  • Will titanium corrode in seawater?

Scope of Thermodynamics

• Thermodynamics is related to the Greek words therme (heat) and dynamikos (power or movement)
• Thermodynamics defines heat, identifying it as energy transfer from one region to another across a temperature gradient
• Thermodynamics addresses energy conservation, plus conversion to other forms or work
• Thermodynamics examines behavior and interactions between systems and surroundings
• Principles are in four laws: zeroth, first, second, and third
• Microscopic approach describes material by microscopic variables of all particles in the system
• Too many particles (NA = 6.022×1023 mol-¹) make this approach impractical
• Macroscopic (Classical) thermodynamics describes material in terms of variables, such as temperature, internal energy or pressure
• Statistical thermodynamics connects classical thermodynamics with microscopic constituents of matter (atoms and molecules)
• This course focuses on classical thermodynamics, with some elements of statistical thermodynamics in discussing entropy

Four Laws of Thermodynamics

• Systems in mutual thermal equilibrium have the same temperature – 0th Law
• A property of the universe, energy, cannot change - 1st Law
• A property of the universe, entropy, can only increase - 2nd Law
• There is an absolute temperature scale with a minimum (absolute zero) and all substances have the same entropy - 3rd Law

System, Surrounding, Boundary and Properties

• The system is the part of the universe being investigated in detail
• Surroundings are the part of the universe outside the system that may interact, exchanging energy or matter
• The system may perform work on the surroundings or have work performed on it
• Interactions occur through a wall or boundary between system and surroundings
• In simple thermodynamic systems, surroundings interact solely through pressure and temperature changes. Composition stays constant
• In materials science and engineering, thermodynamic principles generally apply to chemical reaction systems
• Properties are needed to define a system's condition and surroundings
• The piece of solid cadmium is System A in the example described
• Surrounding I is the ambient pressure and temperature of the laboratory in the example described
• Surrounding II is the atmosphere in a furnace at ambient pressure and 545°C in the example described
• The thermodynamics database about cadmium determines it's melting point is 321°C and vaporization temperature is 767°C in the example described
• In the example, the final equilibrium state in its new surroundings is liquid cadmium

Thermodynamic Systems and Processes

• In an isolated system there is no energy and no matter passed through the boundaries (ex Universe)
• In a closed system energy can pass, but matter cannot pass through the boundaries (ex Free Pinball Machine)
• In an Adiabatic system, No heat can pass through the boundaries (and therefore no matter that can carry heat) (ex Perfect Thermos)
• In an open system both energy and matter may be passed through the boundaries (ex Aquarium)
• Adiabatic appears in both the definitions of systems and processes
• Adiabatic systems have adiabatic boundaries, and cannot conduct heat
• An adiabatic process occurs without transfer of heat
• A process is adiabatic when no heat passes through the boundaries of the system
• A process is isochoric when no work is transferred to the system from its surroundings
• A process is isothermal when the temperature remains constant
• A process is isobaric when the pressure remains constant
• A process is isosomething when something remains constant

Extensive and Intensive Properties

• Properties are either extensive or intensive
• Extensive properties have values that depend on system size
• Intensive properties are independent of system size
• Volume is extensive; temperature and pressure are intensive properties
• Extensive properties, like volume per unit mass (specific volume) and volume per mole (molar volume), are independent of size
• PV' = nRT, where V is volume, applies to n moles of an ideal gas
• PV = RT, where V is molar volume, equals V/n

The Concept of State

• The most important concept in thermodynamics is that of state
• If it were possible to know the masses, velocities, positions, modes of motion of constituent particles in a system, this information would describe the microscopic state of the system
• In the absence of such detailed knowledge needed to determine the microscopic state of the system, thermodynamics begins with a consideration of the properties of the system
• Properties of the system when determined, define the macroscopic state is that all of the properties are fixed
• When the values of a small number of thermodynamic variables are fixed the values of the rest of the thermodynamic variables are also fixed
• For a simple system of fixed composition fixing the values of two thermodynamic variables fixes the values of the rest

Concept of State, independent, state space, and process example

• Only two thermodynamic variables are independent
• The thermodynamic state is uniquely determined when two independent variables are fixed
• This concept is called the Duhem postulate
• The point in a V-P-T space represents equilibrium states
• The mathematical relationship between V, P and T is called an equation of state
• Volume V of a fixed quantity of pure gas depends on values of P and T, so V=V(P,T) in the case of P and T as independent variables
• Moving gas from state 1 to state 2 changes its volume, ΔV = V2 – V1
• The volume change is independent of the path taken
• Constant pressure P1 occurs going from 1 to a
• Constant temperature T2 occurs going from a to 2
• The change in volume depends only on the volumes at states 1 and 2 (dV)

Equilibrium

• A fixed quantity of gas in a cylinder with a movable piston has a simple system
• The system is at rest (equilibrium) when the gas pressure exerted by the gas equals the pressure exerted by the piston
• In this case, the temperature of the gas equals that of the surroundings
• The cylinder’s boundaries also must be diathermal
• The state of the gas is fixed, and equilibrium occurs when balance is achieved between tendencies towards change in the system and tendency to resist change
• Fixing the pressure of the gas at P1 and temperature at T1 determines the state and the volume at the value V1
• With constant temperature and by increasing the weight placed on the piston leads to a pressure exerted on the gas that is increased to P2
• The pressure exerted by the piston on the gas maintained its constant and the temperature of the surroundings is raised from T1 to T2
• cylinder wall causes the transfer of thermal energy from the surroundings into the gas
• Increased 10° temperature increases gas expansion and pushes the piston out of the cylinder
• It is uniformly at temperature T2, the volume of the gas is V2
• The expansion performs work on the piston
• Volume is a state function, so the final volume V2 will be the same if the state started at 1, changed to a, then from a to 2

Ideal Gas Equation of State

• In 1660, Robert Boyle determined experimentally at constant temperature that P varies as 1/V
  • The equation for that is P α (1/V) this is now known as Boyle's Law
• In 1787 Jacques-Alexandre-Cesar Charles determined the volume-temperature relationship at constant pressure
  • The equation for that is V α T this is now known as Charles' law
• Sections of the P-V-T surface at constant T produce rectangular hyperbolae as it approaches the P and V axes
• Sections of the surface at constant P produce straight lines
• In 1802 Joseph-Luis Gay-Lussac observed that the thermal coefficient of what were called "permanent gases" was a constant
• The thermal expansion coefficient, is defined as the fractional increase with temperature at constant pressure, of the volume of a gas at 0° C; that is α = (1/V0 ) (∂V/∂T)P
• Gay obtained a value of 1/267, but refined experiments by Regnault in 1847 showed α to have the value 1/273
• Gases with lower boiling points obey "Boyle's" and Charles' laws more closely than gases with higher boiling points
• Inventing a hypothetical gas obeys Boyle's and Charles' laws exactly at all temperatures and pressures yields a perfect/ideal gas
  • The α value of the ideal gas is alpha=1/273.15
• The finite coefficient of thermal expansion limits the thermal contraction of the ideal gas, that is α equals 1/273.15
• The fractional decrease in the gas volume, per degree decreases 1/273.15 of the volume at 0°C
• 273.15°C is the limit of temperature decrease, as the volume of the gas is zero
• This defines an absolute scale of temperature.
  • The ideal gas temperature scale relates to the arbitrary Celsius scale by equation gives PV/T = PoV/To = constant

Gas Constant

• From Avogadro's (Lorenzo Avogadro 1776-1856) hypothesis, the volume per gram-mole of all ideal gases at 0°C and 1 atm pressure (termed standard temperature and pressure [STP]) is 22.414 liters
• The constant value is PoVo/To = (1 atm * 22.414 liters)/(273.15 Kmole) =0.082057 literatm/degree*mole
• This has the symbol R = gas constant
• It applies to all ideal gases, is a constant
• Resulting in PV = RT this is the equation of state for 1 mole of ideal gas.
• This Equation is called ideal gas law
• The ideal gas is used extensively as a system in thermodynamic discussions

Units of Energy and Work

• The “liter-atmosphere” occurring as the units of R is an energy term
• Work is done when a force moves through a distance, and work and energy have the dimensions of force distance
• The unit of energy in S.I. is the joule
• This work is done when a force of 1 newton moves a distance of 1 meter
• Converting liter atmospheres to joules: 1 atm = 101,325 newtons/meter²
• Multiplying both sides by liters (10-³ m³) gives 1 liter * atm = 101.325 * newton * meters = 101.325 joules
• R = 0.082057 liter · atm/degree · mole = 8.3144 joules/degree mole
• A gram-mole (g-mole/mole) of a substance is the Avogadro # of molecules expressed in grams

Equilibrium Phase Diagrams and Thermodynamics Components

• Equilibrium phase diagram is a graphical representation of temperatures, pressures, composition, or other variables where specific phases exist at equilibrium
• Systems are categorized by component counts
  • One-component (unary)
  • Two-component (binary)
  • Three-component (ternary)
  • Four-component (quaternary)
• The relationship in three areas, are designated as solid, liquid, and vapor.
  • Area AOB is equilibrium state of liquid water
  • Area COA is equilibrium state of solid water
  • Area COB is equilibrium state of water vapor
• This schematic representation part of the pressure-temperature equilibrium phase diagram example is H2O
  • The melting point is designated as m and the boiling point is as b
• Equilibrium is considered homogeneous within the one area
• States are called heterogeneous, such as with the solid and liquid on Curve AO coexisting in equilibrium
  • Liquid and vapor on Curve BO coexisting in equilibrium
  • Vapor and solid on Curve CO is in equilibrium
• The triple point is when the three-phase solid+liquid+vapor meet where P and T are the most unique
• Alloys may be single or multi phase
  • A single phase crystalline alloy consists of 2 or more components that are distributed randomly on a single crystal structure
  • Single-phase alloys are called solid solutions
• The provided phase diagram is a typical simple binary phase diagram
• Below the melting temperature of Al2O3 (2050°C), solid Al2O3 and solid Cr2O3 are completely miscible and both form a solid solution
• Includes ares of complete solid and liquid solubility
• Solid and liquid solutions coexist in equilibrium in the phase
• For Al2O3-Cr2O3 system at the temperature Ti, where the system compositions are between X and Y exist as a two-phase
  • Includes liquid solution of composition /and a solid solution of composition s .

Summary

• In thermodynamics, the universe is divided: the system which of interest to us and surroundings
• There might be several kinds of walls between the system and the surroundings, and they have specific characteristics
• In thermodynamics, the object of interest is the equilibrium of a system
  • If it is fully described, we can know of the state of the system is likely to change as well as determining the particular direction where such action will probably go
• A system (simple) is defined by both pressure and temperature, or, 2 intensive variables, will be independent to some extent
• Other thermodynamic will have, as for pressure/temperature functions, graphs of the independent variables might display the equilibrium states of the systems will display such functions
• The intense variable called a Zeroth Law of Thermodynamics has a temperature referred by T
• First Thermodynamics Law asserts that the energy of the universe can only be a constant and is the different versions that could be generated from it and the extensive variable in internal energy referred by U
• 2nd Law of Thermodynamics relates that process, which is spontaneous, and introduces the extensive variable of entropy referred by S stating it can never decrease
• The 3rd Law of Thermodynamics asserts of zero entropy as temperature levels out toward zero, if the system in thermal equilibrium is complete