Thermodynamics

Thermodynamics

• Science of thermodynamics initiated the Industrial Revolution in the late 1700s/early 1800s.
• Horses then performed heavy labor (horsepower).
• Heat engines and thermodynamics sought to maximize heat engine efficiency as a new invention.
• Modern heat engines are a successful science.
• The Bugatti Veyron, the fastest production car, has 883 kilowatts/1184 brake horsepower and goes 268 miles/hour.

Thermodynamic System

• A thermodynamic system constitutes any delineated part of the Universe.
• It can be as simple as a beaker of water or as complex as an entire galaxy.

Thermodynamic Surroundings

• Thermodynamic surroundings encompass everything outside the thermodynamic system.
• The surroundings constitute the universe outside the system.

The Universe

• The universe constitutes the system plus its surroundings.

The Vastness of the Universe

• The Milky Way is one of billions of galaxies.
• Scientists mapped ~100,000 galaxies near the Milky Way, finding they're part of the Laniakea supercluster.
• The observable Universe exists within a sphere of radius 4.66 x 10^10 light years.
• One light year equals 9.46 x 10^15 meters.

Thermodynamic Surroundings

• The thermite reaction is intensely exothermic, still used today for remote railway line welding: Fe2O3 + 2Al → 2Fe + Al2O3.
• Supernova explosions represent the most violent energetic processes when dying stars explode.
• Impact of supernova explosions on distant galaxies is negligible.
• Surroundings are considered infinite, maintaining constant temperature and pressure.
• This assumption relies on the vast size of the universe.

Boundary Conditions

• Boundaries can be actual or notional.
• Boundaries control the transfer of work, heat, and matter between the system and surroundings, and vice versa.
• Boundaries may or may not restrict such transfers.

Open, Closed, and Isolated Systems

• Open Systems: May exchange both energy and matter with the surroundings; allows for composition changes.
• Closed System: May exchange energy, but not matter, with the surroundings; pressure build-up is a distinct possibility.
• Isolated System: Exchanges neither energy nor matter with its surroundings; pressure build-up is a possibility.

Diathermic and Adiabatic Systems/Walls

• A diathermic system allows heat flow in/out.
• An adiabatic system prevents heat flow in/out.

Isothermal, Isobaric, and Isochoric Processes

• Isothermal implies constant temperature, T.
• Isobaric implies constant pressure, P.
• Isochoric implies constant volume, V.

State Function

• A state function describes the state of the system.
• State functions include: Pressure (P), Volume (V), Temperature (T), Mass (m), Quantity (n), Internal Energy (U), Enthalpy (H), Entropy (S), Gibbs Energy (G).

Path Functions

• The current state of a system is described by a state function.
• The system's path to its particular state is irrelevant.
• Functions that govern transition between states are path functions.
• Heat (q) and work (w) represent forms of energy.
• The state of a changes when energy is supplied or removed as heat or work.

Heat and Work Conventions

• Path functions are positive when energy enters the system.
• Path functions are negative when energy exits the system.
• Heat supplied to the system is qin
• Mechanical work done on the system is Won.

Laws of Thermodynamics

The Zeroth Law of Thermodynamics

• The Zeroth Law was named ironically as it was the last of 4 to be discovered.
• It describes the true meaning of temperature.

The First Law of Thermodynamics

• Rudolf Clausius developed it around 1850.
• It adapts the Law of Conservation of Energy for Thermodynamic Systems.
• It defines the change in the state function (internal energy) based on the flow of energy in/out.
• It defines a new state function called enthalpy.

The Second Law of Thermodynamics

• Rudolf Clausius developed it around 1850, influenced by Sadi Carnot's 1824 work.
• It describes the direction of spontaneous processes, where a hot object loses heat to its surroundings.
• Entropy is a new state function which fundamentally measures disorder.

Third Law of Thermodynamics

• German chemist Walter Nernst developed it in 1912.
• It considers matter at absolute zero.
• It leads to the definition of zero on the entropy scale; determines absolute entropy.

The Zeroth Law of Thermodynamics

Measurement of Temperature

• Thermometers measure temperature routinely.
• The Zeroth Law describes what happens when two objects are separately in thermodynamic equilibrium with a third object.
• Separately in a state of thermodynamic equilibrium, the two objects are in equilibrium with each other.
• Whenever two objects are in contact, energy spontaneously flows between them until they reach thermodynamic equilibrium.
• At a single temperature is reached, it's said that they are in the same temperature.
• Measurement of temperature with thermometers have vital ramifications in our understanding.
• The statement of The Zeroth Law is obvious, but it explains why it wasn't stated until the three main laws; its value is commonly overlooked.

The First Law of Thermodynamics and Enthalpy

• Developed by Rudolf Clausius in 1850.
• The Law of Conservation of Energy states that energy can neither be created nor destroyed; rather, it transforms from one form to another.
• Every thermodynamic system possesses internal energy (U).
• ∆U = qin + Won
• Chemical work occurs during chemical reactions, where the equation is: Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g)
• Chemical work occurs as emerging gas performs.

The Work Done by an Expanding Gas

• w = Fd
• p = F/A
• F = pA
• w = pAd
• w = p∆V
• WOn = -p∆V

The First Law of Thermodynamics

• ΔU = qin + won
• won = -pΔV
• ΔU = qin - pΔV
• Expansion work depends on p and Δ
• For Free Expansion: ΔU = qin - pΔV; but in space p = 0 and ΔU = qin
• Few experiments can be carried out in space, so free expansion is limited in scope.

Reactions at Constant Volume (Domain of Heavy Industries)

• ΔU = qin - pΔV; but at constant volume ΔV = 0 and ΔU = qv.
• Constant volume reactors require the reactants "withstand massive pressure changes", making them expensive.

Reactions at Constant Pressure (Domain of Chemists)

• ∆U = qin -p∆V which means ∆U + p∆V = qin at constant pressure.

• Enthalpy, a new state function, is defined: H = U + pV

• Change in enthalpy: ∆H = ∆U + ∆(pV), and given the product rule is followed:

• ∆H = ∆U + p∆V + V∆p; and the pressure at constant pressure is 0:

• ∆p = 0, V∆p = 0

• ∴ ∆H = ∆U + p∆V

• Therefore ∆H = qp

Ideal Gas Vs Real Gas

• Ideal gas behavior: Follows gas laws; adheres completely to kinetic molecular theory.
• Occupies zero volume, and possesses no attractive forces.
• A "true ideal gas" does not exist.
• A "real gas" does not behave according to the kinetic molecular theory.

Van der Waals Equation

• The magnitude of the deviations from ideality is greatest for the gas at 200 K and least for the gas at 1000 K .
• PV/RT is plotted against pressure for 1mol of gas at three separate temperatures
• An ideal gas would value 1 for that ratio at all temperatures and pressures, making the graph simply a "horizontal line."

Reversible Isothermal Expansion of an Ideal Gas

• Leads to a maximized amount of work being performed by the gas.

Ideal Gas Equation

• PV = nRT
• P = Pressure
• V = Volume
• T = Absolute temperature measured in Kelvin
• n = Quantity
• R = Ideal gas constant equal to 8.314 J K^-1 mol^-1

Isothermal Expansion

• External Pressure p = 2478pa which means Volume is equal to one cubed meter.
• The gas pressure suddenly drops to 826 Pa.
• A perfect ideal gas equation fits perfectly during expansion.
• The gas performs the work during its expansion, the system is performing the work.
• How to change the expansion, so that more work performed while expanding?

WOn for Reversible Isothermal Expansion

• Won = -pdV (From previous slides)

• pV = nRT - p = (nRT)/v

• Won = -(NRT/v) dv

• Reversible change constitutes a theoretical construct.

  • Determines maximized possible expansion work.

Heating Objects: Heat Capacity

• Heat capacity is heat energy, is required to raise the temperature by one degree Celsius or one Kelvin.
• Heat capacity C is measured in joules per kelvin (J/K) and is determined by the equation: C= q/ΔT

Intensive and Extensive Properties:

• Extensive Properties depend on the amount of matter in a sample
• Some examples are weight, length, volume and entropy
• Intensive Properties don't depend on amount of matter in a sample
• Some examples are temperature, boiling point, concentration and luster.

Heat Capacity Definitions

 -  Heat Capacity:  C = q/ΔT
 - Heat capacity is an extensive property.
-  Specific Heat Capacity: Cs = C/m, Measured in units of J K^-1 kg^-1
    - C is heat capacity
    - m is mass
-  Molar Heat Capacity:  Cm = C/n, Measured in units of J K^-1 mol^-1
    -   C   is heat capacity
    -   n   is moles
- Specific Heat Capacity and Molar Heat Capacity are both intense properties.

• Substances and their specific heat capacities (J K⁻¹ kg⁻¹):
  • Graphite: 710
  • Gold: 130
  • Rubber: 2010
  • Polystyrene: 880
  • Wood: 2000
  • Human Skull: 440
  • Paper: 1340
  • Diamond: 520
  • Mercury: 140
  • Copper: 390
  • Sulfur: 710
  • Teflon: 1670

Isochoric and Isobaric Heat Capacities

 -     Cv ​= qv​ /ΔT = ΔU/ΔT
      -     Cv​ is the specific heat at constant volume (isochoric)
        -      qv​ is the heat added at constant volume
    -   Cp = ​qp /ΔT = ΔH/ΔT
        -      Cp is the specific heat at constant pressure (isobaric)
        -     qp​ is the heat added at constant pressure

Cp,m and Cv,m Relationship for Ideal Gas

• Hm = Um +PVm
• For an ideal gas PVm = nRT
• PVm = RT
• Hm = Um + RT RT = 8.314 J K^-1mol^-1 x 298 K ~ 2.5 kJ mol^-1

Because of this its not negligible for Gas.

CP,M & CV,M Relationship for an Ideal Gas

      - Cp = specific heat at constant pressure, and Cv = specific heat at constant volume
 Hm = Um + RT

• For a change in temperature: ΔT ΔHm = Um + RΔT ΔHm /ΔT=ΔUm/ΔT + R Cp,m = Cv,m + R

Second Law of Thermodynamics

- the Second Law was Stated by Rudolph Clausius in 1854.
- Heat Transfer Heat can never pass from a colder body to a warmer body without having something connected and therewith that occur at the same time.
- Defines a new state function, entropy (S), is considered measure of disorder of system: .
    -S = qrev/T

Second Law Real World

• ΔSRT = grev/T

  • ΔSRT = 596 J/ 298 K = 2 J K-1

  ΔSHot = qrev/T --(-596 J/596 K = -1 J/K

Therefore 596 J of heat pass from the hot copper bar to the copper bar at room temperature.

ΔS= -1 (-1J K-1 + 2 J K-1) = 1 J K-1

Spontaneity

• When processes are spontaneous entropy of the universe must increase and gibbs energy of the system must decrease.

Spontaneous Change

• All chemical processes require activation energy.

  • A spontaneous change is one that happens without a constant source of energy from outside the system.

-If a change is spontaneous, in one particular direction, then it will be non-spontaneous, meaning the surroundings supply constant energy, in the reverse direction.

Spontaneous Processes

• Spontaneous processes proceed in one direction.
• Non-spontaneous processes reverse that directions.
• Some temperatures render processes as spontaneous, while other temperatures make them non-spontaneous.

ΔH Does Not Predict Spontaneous Change

• ∆H does not predict spontaneity because a spontaneous reaction can be endothermic or exothermic.
  • Spontaneous Exothermic Processes Include:
    • condensation & freezing at low temperatures.
    • combustion reactions.
    • oxidations of iron and other metals.
  • Spontaneous Endothermic Processes Include:
    • melting & vaporization at high temperatures.
    • dissolving of most soluble salts.

Entropy

• Isolated systems always have increases of entropy.

• Determining the probability of gas contraction.

• Calculate the probability of a 1% contraction of one mole of gas for short amount of time: The total lifetime Universe.

• Finding Probability; each to be found in 99% its original Volume = 99%, (0.99)

  - probability for ONE mole: 0.99*NA
  

Entropy

• Coined by Rudolf Clausius within the 19th century.
• Entropy quantifies a system's randomness.
• Relates ultimately to how molecules move around internally.

Entropy and Thermodynamics

• ΔS must be greater than 0 for a spontaneous process to occur. ΔS univ = ΔS sys + ΔS surr

There is no absolute 0 point for enthalpy, But there is a Zero point for Entropy.

Third Law of Thermodynamics

• There is a zero entropy amount for "the perfect crystal", and therefore entropy can be measured. Increasing Temp= Increasing Entropy

Factors that affect Entropy

a) Temperature -For any Substrance: -S increasing with increasing temp.

B) Entropys depend on physical state

• 5degree increase as phase goes, solid.==>liquid,==>gas

c) Formation of solution.

d) Entropys relation to atomic size complexity etc. - (use same physcial states or comparing).

• Entropy changes during phase transitions from solid to liquid to gas.

Entropy and Structure

• Allotropes of the higher form S, allow atom more freedom.

  • Graphite’s S° = 5.69 J/mol*K
    • Diamond's S°= 2.44 J/mol* K

“ Graphite FE has less FE than Diamond, meaning the translation into Graphite in ring will likely not occur in your time, due the conversion spontaneousness”

Using Entropy Value Chart

• • particles has more freedom can disperse their kinetic energy **

( having more particles increase entropys

• entropy increases with rising temperature.

Entropy Changes in the System

△S=ΣmS productrxn --ΣnHreactant - m AND N represent amounts of products and reactants balanced reaction. The coefficients.

Calculating the Standard Entropy of Reaction, AS

• C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(l)
  • S° (C₃H₈) = 269.9 J/K mol
  • S° (O₂) = 205.0 J/K mol
  • S° (CO₂) = 213.7 J/K mol
  • S° (H₂O) = 69.9 J/K mol

Therefore: ΔS = ΣmS product rxn --ΣnHreactant --[m01] (2000 x -374 J/K

Entropy Changes in the Surroundings

• Entropy (the surrounding) is the system. In surround, functions can heat up or decrease. In surroundings where processes exothermic heat, the system releases energy, leading to "more stability

  • the qsystem is at negative
    • And surrounding, & AS surrounding is at “positive” -- The system in surrounds that processes in “Endo” thermal systems. Provide heat to “absorb” and decrease
    • q system “positive’ And Surrounds are:
  • q is positive
  • is negative
  • S also be low.

Temperature that which Heat is Transferred

q sys=-q aurr the heat "transferred" is "specific"for the reaction and same. -- regardless temperature surroundings

• ΔS surr=- qsys/T

ΔΗ SYS constant p constant ( P )

∆Ssurr = Delta H/temp sys:

• and heat + work be transfer into internal energy - at 290K

Determining Reaction Spontaneity

• The creation at Ammonial and the results at -277

• The reaction between and “spontaneously and temp.

Numericals(Solid & Liquid System)

• find increase of molar enthalpy when it’s heated from 125 to ,927 - - " given molar specific heat of copper(C p

• find the "What enthalpy when tin is heated from 23 to 37c

Given “MELTING” point tin of 505g/ cal

 - " latent heat = 14

 - “what is heat that is “liquid” 55 = respective

Numericals (Gaseous System)

• *“would increase enthalpy *18m0

     - “What is the * of * "
  

• • Given: cv “-3.5 cal & at 28c

    • Calculate *  “transferred “state
      

    • What  5 & pressure to !3x “
      

• "What * at state enthalpy =

  • 5 cal “INITIALLY

      - " 423
    
          - “” calculate this”"””*
    

Universal Entropy and Gibbs Energy

• "energy that follows surrounds… 10
  • The system
• surrounding system and or system to the change - is the same “ " (temp is temp but there's internal heat)
• heat a pressure + constant

Universal Energy is equation; Is:

∆S "universe" = * + " - "

• • energy * or + energy all that is

• “internal” is - ( is all * heat that is “constant”

• therefore with * “

Universal Entropy

• • in Gibbs free that is = 0- = 8417

• Is:

• *is an energy all with and - energy””.

ΔU :

" “is therefore with “ and “ in 18x all” to and “”.

*Exothermic vs. Endothermic Reactions

• *H-ve AS +ve --> spontaneously for all temp

• all are - = at 19000 to internal = “

• • T = AH/AS therefore

= to 27

  - and the internal reaction “does + start + spontaneous to “room”
  - only “ at 1.6 0

Chemical Equilibrium

• The * Gibbs enthalpy *AG. May interpreted of internal between reactants - Therefore: g to ( and /or and to to =

• 18d/ Chemical Potential all *

• • therefore the equilibrium is: A" * = to and B

    All under internal

Chemical Potential µ

• Using: "M"i = m + RT Im all *

##Thermodynamic Equilibrium ∆G =A,G +R71n* = to ≯G+ RT1n*

" is reaction / “ .

• The At equilibrium of the activity constant Is zero
• At “ the “internal”

What note of Activities!

• ACTIVIES the dimensions AND are thermodyamic at all times”

  Therefore :

  : : are replaced the - is all the constants"

• ** The 3rd law of Thermodynamics, at absolute aero**

_ The internal always has its and *

I hope these study notes were helpful!