18Thermodynamics

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TERMS USED IN THERMODYNAMICS
▢ System: Specific part of universe / specified portion of matter under experimental investigation.
▢ Surrounding: Rest part of universe other than system.
▢ Boundary: Anything separating system and surrounding; real / imaginary; rigid / non-rigid; conducting / non-conducting.
▢ Example:
❖ Beaker Reaction:
  • •
    Contents of beaker = system
  • •
    Beaker = boundary
  • •
    Outside beaker = surrounding
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TYPES OF SYSTEM
▢ On Basis of Exchange of Energy and Matter:

Table 1: Open, closed and isolated systems

Type
Exchange with surrounding
Boundary
Example
Open system
Mass + energy
Not sealed, not insulated
Ice in open beaker
Closed system
Energy only; no mass
Sealed, not insulated
Ice in closed beaker
Isolated system
Neither mass nor energy
Perfectly insulated
Ice in thermos flask
▢ On Basis of Composition:

Table 1: Homogeneous and heterogeneous systems

Type
Meaning
Examples
Homogeneous system
Completely uniform throughout; one phase only
Pure single solid, liquid, gas; mixture of gases
Heterogeneous system
Not uniform throughout; two or more phases
Ice + water; insoluble solids + liquid
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THERMODYNAMIC PROPERTIES

Table 1: Extensive vs intensive properties

Property
Depends on amount?
Effect of changing mass
Examples
Extensive property
Yes
Changes with mass
Mass, weight, volume, energy, work, internal energy, enthalpy, entropy, moles, free energy
Intensive property
No
Unchanged with mass
Temperature, pressure, density, concentration, viscosity, refractive index, surface tension, specific heat
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STATE FUNCTIONS
▢ Definition: Thermodynamic parameters depending only on initial and final states; independent of path.
▢ Examples:
  • •
    Internal energy ((E))
  • •
    Enthalpy \((H)\)
  • •
    Entropy \((S)\)
  • •
    Free energy \((G)\)
  • •
    Pressure \((P)\)
  • •
    Temperature \((T)\)
  • •
    Volume \((V)\)
▢ Not State Functions:
  • •
    Work
  • •
    Heat
▢ Reason: Work and heat depend on path followed, not merely initial and final states.
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INTERNAL ENERGY
▢ Definition: Total energy stored in a substance due to chemical nature.
▢ Also Called: Intrinsic energy.
▢ Components:
    ◉ _*type: bullet
  1. Translational energy
  2. Vibrational energy
  3. Rotational energy
  4. Chemical bond energy
  5. Electronic energy
  6. Nuclear energy
  7. Intermolecular potential energy
▢ Formula: \(E = E_t + E_v + E_r + E_e + E_n + E*{PE}\)
▢ Important Points:
  • •
    Internal energy is state function.
  • •
    Depends only on state of system.
  • •
    Independent of method by which state is attained.
  • •
    Absolute value of internal energy cannot be determined.
  • •
    Change in internal energy \((\Delta E)\) can be determined experimentally by bomb calorimeter.
  • •
    \(\Delta E = E_P - E_R\)
  • •
    Internal energy depends on quantity of substance; extensive property.
  • •
    Internal energy of ideal gas depends only on temperature.
  • •
    Isothermal ideal gas process: \(\Delta E=0\).
  • •
    Isochoric process: \(Q_v=\Delta E\).
  • •
    Adiabatic expansion of gas causes cooling due to decrease in internal energy.
  • •
    Reversible cyclic process: \(\Delta E=0\).
  • •
    Element in most stable form: internal energy conventionally zero.
▢ Monoatomic Gas: \(E = \dfrac{3}{2}RT\,KJ\,mol^{-1}\)

Table 1: Internal energy change and reaction nature

Condition
\(\Delta E\)
Reaction type
\(E_1>E_2\) or \(E_R>E_P\)
Negative
Exothermic
\(E_1
Positive
Endothermic
▢ Units:
  • •
    \(1\,calorie = 4.186\,J\)
  • •
    \(1\,Joule = 10^7\,erg\)
  • •
    \(1\,litre\,atm = 101.3\,J\)
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THERMODYNAMIC PROCESSES
▢ Definition: Operation by which thermodynamic system changes from one state to another.
▢ **table:
    ▢ Isothermal Expansion Work:
      ◉ **type: bullet
    1. \(W*{max}=2.303\,nRT\log*{10}\dfrac{V_2}{V_1}\)
    2. \(W*{max}=2.303\,nRT\log*{10}\dfrac{P_1}{P_2}\)
    ▢ Adiabatic Process:
    • •
      \(q=0\)
    • •
      Fast process
    • •
      Closed insulated container / thermos bottle
    • •
      Expansion → temperature decreases
    • •
      Compression → temperature increases
    ▢ Cyclic Process:
    • •
      \(\Delta E=0\)
    • •
      \(\Delta H=0\)
    📚
    WORK AND HEAT
    ▢ Work:
    ❖ Definition: Mode of energy transfer from or to a system with reference to surroundings.
    ❖ General Formula: \(W = F \times d\)
    ❖ Types:
    • •
      Electrical work
    • •
      Mechanical / pressure-volume work
    ❖ Electrical Work: \(\text{Electrical work} = EMF \times \text{Quantity of electricity}\)
    ▢ Mechanical Work:
    ❖ Definition: Pressure-volume work done when system changes volume against external pressure.
    ❖ Formulae:
      ◈ **type: bullet
    1. \(W=P\int*{V_1}^{V_2}dV\)
    2. \(W=P(V_2-V_1)=P\Delta V\)
    3. \(P=P*{ext}\)
    ❖ Expansion:
    • •
      \(V_2>V_1\)
    • •
      Work done by system on surrounding
    • •
      \(W=-P\Delta V\)
    ❖ Compression:
    • •
      \(V_2
    • •
      Work done on system
    • •
      \(W=+P\Delta V\)
    ❖ Vacuum Expansion: If \(P=0\), then \(W=0\).
    ❖ Maximum Work: Maximum work during gas expansion occurs when process is isothermal and reversible.
    ❖ Isothermal Reversible Expansion: \(W=-2.303\,nRT\log\dfrac{V_2}{V_1}=-2.303\,nRT\log\dfrac{P_1}{P_2}\)
    Negative work
    Negative sign of work indicates expansion / work done by system.
    ▢ Heat:
    ❖ Definition: Mode of energy exchange due to temperature difference between system and surroundings.
    ❖ Symbol: \(Q\)
    ❖ Sign Convention:
    • •
      Heat given by system → negative sign
    • •
      Heat absorbed by system → positive sign
    ❖ Unit: SI unit = joule.
    ❖ Calorie: Heat required to raise temperature of 1 g water by \(1^\circ C\).
    ▢ Difference between Heat and Work:
    • •
      Work = organized form of energy.
    • •
      Heat = random form of energy.
    • •
      Work and heat are not state functions.
    • •
      Energy is thermodynamic property; work and heat are not.
    📚
    FIRST LAW OF THERMODYNAMICS
    ▢ Statement: Energy can neither be created nor destroyed; it can only be converted from one form to another.
    ▢ Other Forms:
    • •
      Total energy of isolated system remains constant.
    • •
      When one form of energy disappears, equivalent amount of other form appears.
    • •
      Perpetual motion machine impossible.
    • •
      For every \(4.184\,J\) work done, \(1\,calorie\) heat produced and vice versa.
    ▢ Mathematical Form:
    • •
      \(\Delta E=Q-W\) when work is done by system
    • •
      \(\Delta E=Q+W\) when work is done on system
    ▢ Differential Forms:
    • •
      \(dE=\delta Q-\delta W\)
    • •
      For work done by system: \(dE=\delta Q-PdV\)
    • •
      For work done on system: \(dE=\delta Q+PdV\)
    ▢ Special Forms:

    Table 1: First law under special conditions

    Condition
    Result
    Isothermal reversible process
    \(\Delta E=0\), hence \(Q=-W\)
    Cyclic process
    \(\Delta E=0\), hence \(Q=-W\)
    Isochoric process
    \(W=0\), hence \(\Delta E=Q_v\)
    Adiabatic process
    \(Q=0\), hence \(\Delta E=-W\)
    Gas expansion against external pressure
    \(W=-P\Delta V\)
    Gas compression
    \(W=P\Delta V\)
    Vacuum expansion
    \(P=0\), hence \(W=0\)
    ▢ Limitations:
    • •
      Does not predict spontaneity / feasibility.
    • •
      Does not predict direction of process.
    • •
      Does not explain why heat flows from hot to cold naturally.
    • •
      Does not explain complete conversion of heat into work.
    • •
      Equivalent transformation possible, but heat cannot be completely converted into work without other change.
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    ENTHALPY
    ▢ Definition: Total heat content of a system at constant pressure.
    ▢ Formula: \(H=E+PV\)
    ▢ Properties:
    • •
      State function.
    • •
      Absolute value cannot be determined.
    • •
      \(\Delta H\) can be measured in calorimeter open to atmosphere.
    • •
      Enthalpy of compound = heat of formation, not heat of reaction.
    • •
      Elements in standard state: enthalpy zero.
    ▢ Constant Pressure: \(Q_p=\Delta H\)
    ▢ Signs:
    • •
      Exothermic reaction: \(\Delta H<0\), \(H_R>H_P\)
    • •
      Endothermic reaction: \(\Delta H>0\), \(H_P>H_R\)
    ▢ Monoatomic Gas: \(H=\dfrac{5}{2}RT\,mol^{-1}\)
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    THERMOCHEMISTRY
    ▢ Definition: Branch of chemistry dealing with heat changes accompanying chemical reactions.
    ▢ Thermochemical Equation: Balanced chemical equation showing amount of heat evolved or absorbed.
    ▢ Modern Convention:
    • •
      Heat change represented as change in enthalpy.
    • •
      \(\Delta H=H_P-H_R\)
    • •
      Reactants: \(H_R\)
    • •
      Products: \(H_P\)
    ▢ Reaction Type:
    • •
      \(H_P>H_R\Rightarrow\Delta H>0\Rightarrow\) endothermic
    • •
      \(H_R>H_P\Rightarrow\Delta H<0\Rightarrow\) exothermic
    ▢ Reverse Reaction: Thermochemical equation can be reversed by changing sign of \(\Delta H\).
    ▢ Laplace-Lavoisier Law: Heat absorbed/evolved in a reaction is equal and opposite to heat change when reaction is reversed.
    ▢ Units: Heat contents expressed in calories or joules.
    📚
    HEAT OF REACTION
    ▢ Definition: Amount of heat evolved or absorbed when stoichiometric quantities shown by chemical equation react completely.
    ▢ Standard Heat of Reaction: Heat of reaction under standard conditions; represented by \(\Delta H^\circ\).
    ▢ At Constant Volume:
    • •
      \(Q_v=\Delta E\)
    • •
      Equals change in internal energy
    ▢ At Constant Pressure:
    • •
      \(Q_p=\Delta H\)
    • •
      Equals change in enthalpy
    ▢ Factors Affecting Heat of Reaction:
    • •
      Temperature
    • •
      State of matter: solid, liquid, gas
    • •
      Pressure for gases
    • •
      Concentration of solution
    • •
      Allotrope of solid
    ▢ Standard Conditions:
    • •
      \(T=298K\) / \(25^\circ C\)
    • •
      \(P=1\,atm\)
    • •
      State available at STP
    • •
      Concentration: \(1M\) or \(1N\)
    • •
      Most stable allotrope at STP: C = graphite, S = rhombic, P = white
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    RELATION BETWEEN \(\DELTA H\) AND \(\DELTA E\)
    ▢ Formulae:
    • •
      \(\Delta H=\Delta E+P\Delta V\)
    • •
      \(\Delta H=\Delta E+\Delta n_gRT\)
    ▢ Terms:
    • •
      \(\Delta n_g =\) moles of gaseous products - moles of gaseous reactants
    • •
      \(\Delta E=\) heat of reaction at constant volume
    • •
      \(\Delta H=\) heat of reaction at constant pressure

    Table 1: Effect of \(\Delta n_g\)

    Condition
    Relation
    \(\Delta n_g=0\)
    \(\Delta H=\Delta E\)
    \(\Delta n_g>0\)
    \(\Delta H>\Delta E\)
    \(\Delta n_g<0\)
    \(\Delta H<\Delta E\)
    Only solids and liquids
    \(\Delta H=\Delta E\)
    ▢ Examples:
    • •
      \(H_2(g)+I_2(g)\rightarrow2HI(g)\): \(\Delta n=0\)
    • •
      \(MgCO_3(s)\rightarrow MgO(s)+CO_2(g)\): \(\Delta n>0\)
    • •
      \(N_2(g)+3H_2(g)\rightarrow2NH_3(g)\): \(\Delta n<0\)
    📚
    TYPES OF HEAT OF REACTIONS
    ▢ Standard Heat of Formation:
    ❖ Definition: Heat evolved or absorbed when 1 mole of substance is formed from constituent elements in standard states.
    ❖ Symbol: \(\Delta H_f^\circ\)
    ❖ Standard State: \(25^\circ C\), \(1\,atm\)
    ❖ Important Points:
    • •
      Equation must represent formation of 1 molecule / 1 mole only.
    • •
      Elements in natural state have zero enthalpy.
    • •
      For allotropic element, most stable allotrope has zero enthalpy of formation.
    • •
      Graphite: \(\Delta H_f^\circ=0\); diamond not zero.
    • •
      Rhombic sulphur has zero standard enthalpy.
    ❖ Examples:
    • •
      \(C(s)+O_2(g)\rightarrow CO_2(g);\ \Delta H_f=-94\,kcal\)
    • •
      \(H_2(g)+\dfrac{1}{2}O_2(g)\rightarrow H_2O(l);\ \Delta H_f=-68\,kcal\)
    • •
      \(\dfrac{1}{2}N_2(g)+\dfrac{3}{2}H_2(g)\rightarrow NH_3(g);\ \Delta H_f=-11\,kcal\)
    ▢ Standard Heat of Combustion:
    ❖ Definition: Heat evolved when 1 mole of substance is completely burnt in air or oxygen.
    ❖ Symbol: \(\Delta H_c^\circ\)
    ❖ Example: \(C_2H_6(g)+3.5O_2(g)\rightarrow2CO_2(g)+3H_2O(l);\ \Delta H=-372.8\,kcal\)
    ❖ Important Points:
    • •
      Take 1 mole of substance whose combustion heat is to be determined.
    • •
      Take required oxygen for balancing.
    • •
      C, H, S oxidized to \(CO_2\), \(H_2O\), \(SO_2\) respectively.
    • •
      Heat of combustion is always negative.
    • •
      Used for calorific value of fuels.
    • •
      Greater heat of combustion per gram/cc → more effective fuel.
    • •
      Combustion of organic substances and hydrogenation measured by bomb calorimeter.
    ▢ Standard Heat of Neutralisation:
    ❖ Definition: Heat evolved when 1 gram equivalent acid/base is neutralized by 1 gram equivalent base/acid in fairly dilute solution.
    ❖ Symbol: \(\Delta H_N^\circ\)
    ❖ Strong Acid + Strong Base:
    • •
      \(HCl(aq)+NaOH(aq)\rightarrow NaCl(aq)+H_2O\)
    • •
      \(\Delta H=-13.7\,kcal\)
    • •
      Constant value: \(13.7\,kcal\) or \(57\,kJ\,mol^{-1}\)
    • •
      Actually heat of formation of water from \(H^+\) and \(OH^-\): \(H^+ + OH^-\rightarrow H_2O\)
    ❖ Weak Acid/Base:
    • •
      Part of heat used for ionisation.
    • •
      Heat of neutralisation less than \(13.7\,kcal\,mol^{-1}\).
    • •
      Example: HCN + NaOH: \(\Delta H=-2.9\,kcal\)
    • •
      Ionisation heat of HCN = \(10.8\,kcal\).
    ❖ Measurement: Calorimeter / Dewar flask.
    ❖ Nature: Neutralisation is exothermic.
    ▢ Heat of Solution:
    ❖ Definition: Heat evolved or absorbed when 1 mole solute dissolves completely in excess solvent so further dilution produces no heat change.
    ❖ Examples:
    • •
      \(NH_4Cl(s)+H_2O(l)\rightarrow NH_4Cl(aq);\ \Delta H=+3.90\,kcal\)
    • •
      \(BaCl_2(s)+H_2O(l)\rightarrow BaCl_2(aq);\ \Delta H=-2.70\,kcal\)
    ▢ Heat of Dilution:
    ❖ Definition: Heat evolved or absorbed when solution containing 1 mole solute is diluted from one concentration to another.
    ❖ Example:
      ◈ _*type: bullet
    1. \(KCl(s)+20H_2O\rightarrow KCl(20\,mole);\ \Delta H_1=+3.8\,kcal\)
    2. \(KCl(s)+200H_2O\rightarrow KCl(200\,mole);\ \Delta H_2=+4.4\,kcal\)
    3. \(\Delta H*{dilution}=\Delta H_2-\Delta H_1=+0.64\,kcal\)
    ▢ Heat of Hydration:
    ❖ Definition: Heat evolved or absorbed when 1 mole anhydrous/partially hydrated salt combines with required water to form definite hydrate.
    ❖ Examples:
    • •
      \(CuSO_4(s)+5H_2O(l)\rightarrow CuSO_4\cdot5H_2O(s);\ \Delta H=-18.69\,kcal\)
    • •
      \(CaCl_2(s)+6H_2O(l)\rightarrow CaCl_2\cdot6H_2O(s);\ \Delta H=-18.8\,kcal\)
    ❖ Points:
    • •
      Hydration is exothermic due to bonding between central metal ion and water molecules.
    • •
      Dissolution of anhydrous salt includes hydration + dissolution.
    • •
      \(\text{Heat of solution of anhydrous salt}=\text{Heat of hydration}+\text{Heat of solution of hydrated salt}\)
    • •
      During dissolution physical state changes.
    • •
      During hydration no physical state change.
    ▢ Heat of Dissociation / Ionisation:
    ❖ Definition: Heat absorbed when 1 mole electrolyte completely dissociates into ions.
    ❖ Example: \(CH_3COOH\rightarrow CH_3COO^-+H^+;\ \Delta H=3\,kcal\)
    ▢ Heat of Precipitation:
    ❖ Definition: Heat liberated during precipitation of 1 mole sparingly soluble substance from suitable electrolyte solutions.
    ❖ Example: \(Ba^{2+}+SO_4^{2-}\rightarrow BaSO_4(s);\ \Delta H=-4.66\,kcal\)
    ▢ Heat of Transition: Heat evolved when a substance converts from one allotropic form to another.
    📚
    LAWS OF THERMOCHEMISTRY
    ▢ First Law / Laplace and Lavoisier Law:
    • •
      \(A+B\rightarrow C+D;\ \Delta H=-a\,Kcal\)
    • •
      \(C+D\rightarrow A+B;\ \Delta H=+a\,Kcal\)
    • •
      Sign of \(\Delta H\) changes for reverse reaction.
    • •
      Illustrates conservation of energy.
    ▢ Hess's Law of Constant Heat Summation:
    ❖ Statement: Total heat change accompanying chemical reaction is same whether reaction occurs in one step or several steps.
    ❖ Meaning:
    • •
      Heat of reaction depends only on initial reactants and final products.
    • •
      Independent of intermediate products.
    • •
      Used to find heat of reaction without actual reaction.
    • •
      Reaction equations and heat changes can be added/subtracted.
    ❖ Relation: \(\Delta H=a=x+y+w\)
    📚
    BOND ENERGY
    ▢ Bond Formation Energy: Heat evolved when bond forms between two gaseous atoms to form gaseous molecular product.
    ▢ Bond Energy: Average energy required to dissociate / break bonds of a given type present in 1 mole compound.
    ▢ Example: C-H bond energy in methane = average of dissociation energies of four C-H bonds.
    ▢ Unit: \(kJ\,mol^{-1}\)
    ▢ Use: Calculation of enthalpy change in reactions.
    ▢ Formula: \(\Delta H^\circ=\sum \text{Bond energies of reactants}-\sum \text{Bond energies of products}\)
    📚
    THERMOCHEMICAL CALCULATIONS
    ▢ Heat of Reaction:
      ◉ **type: bullet
    1. \(\Delta H=\text{Heat content of products}-\text{Heat content of reactants}\)
    2. \(\Delta H=\Delta H_P-\Delta H_R\)
    3. \(\Delta H=\sum\Delta H_f(products)-\sum\Delta H_f(reactants)\)
    4. \(\Delta H=\sum\Delta H_c(reactants)-\sum\Delta H_c(products)\)
    5. \(\Delta H=\sum\text{Bond energy of reactants}-\sum\text{Bond energy of products}\)
    ▢ Kirchhoff Equation:
      ◉ **type: bullet
    1. \(\Delta H_2-\Delta H_1=\Delta C_p(T_2-T_1)\)
    2. \(\Delta C_p=C*{p2}-C*{p1}\)
    3. \(C*{p2},C*{p1}=\) molar heat capacities of products and reactants
    ▢ Pressure-Volume Relation:
    • •
      \(\Delta H=\Delta E+P\Delta V\)
    • •
      \(\Delta H=\Delta E+\Delta nRT\)
    ▢ Numerical Results:
      ◉ _*type: bullet
    1. For \(CCl_4(g)+2H_2O(g)\rightarrow CO_2(g)+4HCl(g)\), \(\Delta H^\circ*{298}=-41.4\,kcal\)
    2. Combustion of benzene at constant volume \(=780\,kcal\,mol^{-1}\); heat evolved by 39 g in open vessel \(=390.45\,kcal\)
    3. For \(2C_6H_6(l)+15O_2(g)\rightarrow12CO_2(g)+6H_2O(l)\), \(\Delta H-\Delta E=-7.4\,kJ\)
    4. If enthalpy of neutralisation of HCl with NaOH is \(x\), heat evolved by 500 ml 2N HCl + 250 ml 4N NaOH = \(x\)
    📚
    SECOND LAW OF THERMODYNAMICS
    ▢ Need: Covers limitations of first law.
    ▢ Statements:
    • •
      All spontaneous processes are thermodynamically irreversible.
    • •
      Heat cannot be completely converted into equivalent work without producing change elsewhere.
    • •
      Without external agency, heat cannot pass from colder body to hotter body.
    • •
      Perfect reversible machine working between same source and sink temperatures has same efficiency regardless of substance used.
    • •
      Heat engine can never be 100% efficient.
    • •
      It is impossible to transfer heat from lower temperature to higher temperature without applying work.
    ▢ Special Points:
    • •
      Second law gives concept of entropy.
    • •
      Entropy of universe constantly increases.
    📚
    ENTROPY
    ▢ Definition: Quantity indicating whether chemical/physical change can occur in isolated system.
    ▢ Also: Measure of disorder / randomness of system.
    ▢ Order: \(Gas>Liquid>Solid\)
    ▢ Symbol: \(S\)
    ▢ Properties:
      ◉ _*type: bullet
    1. State function.
    2. For pure crystals, entropy taken as zero.
    3. Entropy change is extensive property.
    4. Units: \(eK^{-1}mol^{-1}\) or \(J K^{-1}mol^{-1}\).
    5. Entropy = measure of unavailable energy.
    ▢ Formulae:
      ◉ **type: bullet
    1. \(\Delta S=\dfrac{Q*{reversible}}{T}\)
    2. \(\Delta S=S*{final}-S*{initial}\)
    3. \(Entropy=\dfrac{\text{unavailable energy}}{Temperature}\)
    ▢ Conditions:
      ◉ **type: bullet
    1. At equilibrium: \(\Delta S=0\)
    2. Cyclic and adiabatic processes: \(\Delta S=0\)
    3. Natural process: \(\Delta S*{universe}>0\)
    4. Spontaneous isolated system: \(\Delta S>0\)
    ▢ Trouton's Rule: \(\Delta S*{vap}\) of most liquids \(=88\pm5\,J\,mol^{-1}K^{-1}\) at normal boiling point.
    ▢ Special Points:
    • •
      Absolute entropy can be determined.
    • •
      Boiling egg → entropy increases.
    • •
      Rubber band stretched → entropy decreases.
    • •
      Water cooled to ice → entropy decreases.
    📚
    CARNOT CYCLE AND HEAT ENGINE
    ▢ Heat Engine: Machine converting heat into work.
    ▢ Efficiency: Fraction of absorbed heat converted into work.
    ▢ Symbols:
    • •
      \(Q_2=\) heat absorbed from source
    • •
      \(Q_1=\) heat returned to sink
    • •
      \(T_2=\) source temperature
    • •
      \(T_1=\) sink temperature
    • •
      \(W=\) work done
    ▢ Formulae:
    • •
      \(\eta=\dfrac{W}{Q_2}\)
    • •
      \(\eta=\dfrac{Q_2-Q_1}{Q_2}\)
    • •
      \(\eta=\dfrac{T_2-T_1}{T_2}\)
    • •
      \(\eta=1-\dfrac{T_1}{T_2}\)
    • •
      \(\dfrac{Q_1}{Q_2}=\dfrac{T_1}{T_2}\)
    ▢ Carnot Engine:
    • •
      Hypothetical heat engine proposed by Carnot.
    • •
      Efficiency depends on source and sink temperatures.
    • •
      Cyclic process yields continuous work.
    • •
      Steam engine is typical heat engine.
    • •
      Source: boiler; sink: surroundings.
    ▢ Numerical Results:
    • •
      Steam engine between \(110^\circ C\) and \(25^\circ C\): efficiency \(=22.2\%\)
    • •
      Boiler raised to \(140^\circ C\), sink same: efficiency \(=27.8\%\)
    • •
      Engine between \(100^\circ C\) and \(0^\circ C\), heat \(453.6\,kcal\): useful work \(=508.8\,kJ\)
    • •
      Carnot cycle between \(95^\circ C\) and \(15^\circ C\), work \(214\,cal\): heat supplied \(=984.4\,cal\)
    📚
    SPONTANEOUS, NATURAL OR IRREVERSIBLE PROCESS
    ▢ Definition: Process proceeding of its own accord without external agency.
    ▢ Key Points:
      ◉ _*type: bullet
    1. All natural processes are spontaneous.
    2. Spontaneous processes cannot be reversed without external agency.
    3. Also called irreversible.
    4. Non-spontaneous process has no natural tendency to occur.
    5. Spontaneous does not indicate rate; process may be fast or slow.
    ▢ Examples:
      ◉ **type: bullet
    1. Water flows downhill spontaneously.
    2. Heat flows from hot body to cold body.
    3. Gas expands from high pressure to low pressure.
    4. Diffusion from concentrated solution to less concentrated solution.
    5. Electricity flows from higher potential to lower potential.
    6. Zn dissolves in \(CuSO_4\) solution and precipitates Cu: \(Zn(s)+CuSO_4(aq)\rightarrow ZnSO_4(aq)+Cu(s)\)
    ▢ Entropy Criterion:
      ◉ **type: bullet
    1. Reversible equilibrium process: \(\Delta S=0\)
    2. Isolated spontaneous process: \(\Delta S>0\)
    3. Non-isolated system: \(\Delta S*{total}=\Delta S*{system}+\Delta S*{surrounding}\)
    4. Spontaneous process requires \(\Delta S*{total}>0\)
    5. \(\Delta S*{universe}>0\)
    📚
    GIBBS FREE ENERGY
    ▢ Definition: Maximum energy available to system during process that can be converted into useful work.
    ▢ Need: Introduced to predict spontaneity / feasibility because enthalpy or entropy alone cannot predict all reactions.
    ▢ Formulae:
      ◉ **type: bullet
    1. \(G=H-TS\)
    2. \(\Delta G=\Delta H-T\Delta S\)
    3. \(\Delta G=G*{product}-G*{reactant}\)
    4. \(\Delta G=\Delta H-T\Delta S\)
    ▢ Gibbs-Helmholtz Equation: \(\Delta G=\Delta H-T\Delta S\)
    ▢ Spontaneity:
    • •
      \(\Delta G<0\): spontaneous
    • •
      \(\Delta G=0\): equilibrium; no net reaction
    • •
      \(\Delta G>0\): non-spontaneous forward; may proceed backward
    • •
      Spontaneous reaction occurs with decrease in Gibbs free energy.
    • •
      Decrease in Gibbs free energy = useful work done.
    ▢ Criteria:
    • •
      Decrease in enthalpy / energy
    • •
      Increase in entropy
    • •
      \(\Delta H<0\), \(\Delta S>0\) → spontaneous at all temperatures
    ▢ Equilibrium Relation:
    • •
      \(\Delta G=\Delta G^\circ+2.303RT\log K\)
    • •
      At equilibrium, \(\Delta G=0\)
    • •
      \(\Delta G^\circ=-2.303RT\log K\)
    ▢ Electrochemical Cell:
      ◉ **type: bullet
    1. \(\Delta G=-nFE^\circ\)
    2. \(n=\) moles of electrons
    3. \(F=96500\)
    4. \(E=E^\circ*{cathode}-E^\circ*{anode}\)

    Table 1: \(\Delta H\), \(\Delta S\), \(\Delta G\) and nature of process

    Case
    \(\Delta H\)
    \(\Delta S\)
    \(\Delta G=\Delta H-T\Delta S\)
    Nature
    1
    -ve
    +ve
    -ve at all temperatures
    Spontaneous at all temperatures
    2
    +ve
    +ve
    -ve at high temperature; +ve at low temperature
    Spontaneous at high temperature; non-spontaneous at low temperature
    3
    -ve
    -ve
    -ve at low temperature; +ve at high temperature
    Spontaneous at low temperature; non-spontaneous at high temperature
    4
    +ve
    -ve
    +ve at all temperatures
    Non-spontaneous at all temperatures
    ▢ Numerical:
    ❖ Problem: For \(A+B\rightarrow C\), \(\Delta H=30\,kJ\,mol^{-1}\), \(\Delta S=60\,J\,K^{-1}mol^{-1}\).
    ❖ Result: \(T=\dfrac{\Delta H}{\Delta S}=500K=227^\circ C\); spontaneous above \(227^\circ C\).
    📚
    THIRD LAW OF THERMODYNAMICS
    📖
    **c
    📝
    Formulated By
    Nernst.
    📝
    Statement
    Entropy of perfectly crystalline solid is zero at absolute zero temperature.
    📝
    Reason
    At absolute zero, perfectly crystalline solid has perfect order of constituent particles.
    📝
    Use
    Calculation of absolute entropy.
    📝
    Exception
    \(NO\), \(N_2O\), \(CO\) etc. do not have zero entropy even at absolute zero because randomness due to dipole moment remains.
    📚
    READ & DIGEST
    📖
    **c
    📝
    Important Points
      ■ **type: bullet
    1. If \(H_R
    2. If \(H_R>H_P\), reaction is exothermic: \(\Delta H=-ve\).
    3. \(NH_4Cl\) dissolved in water makes solution cold; change is endothermic.
    4. Heat exchanged at constant temperature and pressure is enthalpy.
    5. Increasing enthalpy of vaporisation order: \(PH_3, AsH_3, NH_3\).
    6. Greater intermolecular force → higher enthalpy of vaporisation.
    7. For \(N_2+3H_2\rightarrow2NH_3\): \(\Delta H=\Delta E-2RT\).
    8. Hess's law deals with change in heat of reaction. [MOE 2001]
    9. Standard molar enthalpy of formation of \(CO_2\) equals standard molar enthalpy of combustion of carbon/graphite.
    10. Heat of formation of A and B are \(-84\,kJ\) and \(-156\,kJ\); A is less stable than B.
    11. For \(S+\dfrac{3}{2}O_2\rightarrow SO_3+2x\) J and \(SO_2+\dfrac{1}{2}O_2\rightarrow SO_3+y\) J, heat of formation of \(SO_2=(2x-y)\).
    12. Heat of neutralisation is determined by Dewar flask.
    13. Main constituent of natural gas is methane.
    14. Good fuel: high calorific value + low ignition temperature.
    15. Coal is fossil fuel. [MOE]
    16. Plants and living beings are open systems.
    17. Pressure cooker is closed system.
    18. All reactions with chemical dissociation are reversible and endothermic.
    19. In adiabatic process, total heat of system remains constant.
    20. Gas performs no work when it expands isochorically.
    21. P-V indicator diagram parallel to volume axis indicates isobaric process.
    22. At constant temperature and pressure, gas expansion keeps internal energy constant.
    23. Internal energy depends on rotational, vibrational and translational energies; not gravitational pull.
    24. In closed insulated container with stirring paddle: \(\Delta E=\Delta W\ne0\), \(\Delta Q=0\).
    25. Melting ice and evaporation of water are endothermic and spontaneous.
    26. Criterion for spontaneity: \((\Delta S*{system}+\Delta S*{surrounding})>0\).
    27. \(\Delta G^\circ<0\) when system does electrical work on surroundings.
    28. Correct relation: \(\Delta G^\circ=-RT\ln K_c\).
    29. If \(\Delta S*{total}>0\), process is spontaneous. [MOE]
    30. If \(\Delta S*{total}=0\), process is in equilibrium.
    31. If \(\Delta S*{total}<0\), direct process non-spontaneous; reverse may be spontaneous.
    32. If \(\Delta G<0\), process is spontaneous. [MOE/IOM]
    33. If \(\Delta G=0\), equilibrium.
    34. If \(\Delta G>0\), direct process non-spontaneous; reverse may be spontaneous.
    35. Conversion \(P_4\rightarrow P*\alpha\) is exothermic physical change.
    36. Neutralisation of strong acid with strong base liberates constant heat: \(57.3\,kJ\,mol^{-1}\) or \(13.7\,cal\,mol^{-1}\). [BPKIHS]
    37. Heat required to raise temperature of a body by 1 K = thermal capacity.
    38. Opening refrigerator door in room slightly increases room temperature. [I.E. 2011]
    39. Fan switched on in closed room slightly increases room temperature.
    40. Burning tyre decreases temperature.
    41. Thermos flask prevents heat transfer by conduction, convection and radiation.
    42. Shaking tea in thermos flask slightly increases temperature.
    43. For reaction possible at all temperatures: \(\Delta H<0\), \(\Delta S>0\). [MOE 2061]
    44. Reaction not feasible when \(\Delta H=+ve\), \(\Delta S=-ve\). [MOE 2003]
    45. Lavoisier and Laplace law illustrates conservation of energy.
    46. Heat measured in bomb calorimeter = \(\Delta E\).
    47. High heat of formation → less stable compound.
    48. \(C+O_2\rightarrow CO_2\), \(\Delta H^\circ=-x\,kJ\); \(2CO+O_2\rightarrow2CO_2\), \(\Delta H^\circ=-y\,kJ\); enthalpy of formation of CO = \(\dfrac{y-2x}{2}\).
    49. Heat of neutralisation is highest when both acid and base are strong.
    50. At equilibrium, \(\Delta G=0\) under constant T and P.
    51. For exothermic reaction to be spontaneous, temperature must be low.
    52. For \(C+O_2\rightarrow CO_2\), \(\Delta H=\Delta E\) because \(\Delta n=0\).
    53. Work is organized energy; heat is random energy.
    54. \(\Delta H=\Delta E+P\Delta V\) is valid at constant pressure.
    55. Earth is open system with respect to energy; closed system with respect to matter.
    56. Enthalpy of combustion is always negative.
    57. Hess law is used to find heat of reaction, heat of transition, heat of formation.
    58. Compounds with negative heat of formation are exothermic and very stable.
    59. Nernst proposed third law of thermodynamics.
    60. Calorific value of hydrocarbon \(\propto\) number of carbon atoms per mole or molar mass.
    61. During isothermal expansion of ideal gas, entropy remains unaffected: \(\Delta H=\Delta E+P\Delta V=0\).
    62. Thermodynamic standard conditions: \(298K\), \(1atm\).
    📚
    _*MCQ
      1. A well stoppered thermos flask contains some ice cubes. This is an example of a
      2. Closed system
      3. Open system
      4. Isolated system
      5. Non-thermodynamic system
      6. c
        1. Identify the intensive quantity from the following
        2. Enthalpy and temperature
        3. Volume and temperature
        4. Enthalpy and volume
        5. Temperature and refractive index
        6. d
          1. For an adiabatic process, which of the following is correct?
          2. \(P\Delta V=0\)
          3. \(q=+W\)
          4. \(\Delta E=q\)
          5. \(q=0\)
          6. d
            1. All reactions with chemical dissociation are
            2. Reversible
            3. Reversible and endothermic
            4. Exothermic
            5. Reversible or irreversible and endothermic or exothermic
            6. b
              1. According to first law of thermodynamics
              2. \(\Delta E=Q+W\)
              3. \(\Delta E=W-Q\)
              4. \(W=Q+\Delta E\)
              5. None of these
              6. a
                1. Internal energy does not include
                2. Vibrational energy
                3. Rotational energy
                4. Energy arising by gravitational pull
                5. Nuclear energy
                6. c
                  1. Which of the following values of heat of formation indicates that the product is least stable?
                  2. \(-94\,kcal\)
                  3. \(-231.6\,kcal\)
                  4. \(+21.4\,kcal\)
                  5. \(+64.8\,kcal\)
                  6. d
                    1. Compounds with high heat of formation are less stable because
                    2. It is difficult to synthesize them
                    3. Energy-rich state leads to instability
                    4. High temperature is required to synthesize them
                    5. Molecules of such compounds are distorted
                    6. b
                      1. The enthalpy of vaporization from the following two equations is: \(H_2(g)+\dfrac{1}{2}O_2(g)\rightarrow H_2O(l);\ \Delta H=-286\,kJ\), \(H_2(g)+\dfrac{1}{2}O_2(g)\rightarrow H_2O(g);\ \Delta H=-245.5\,kJ\)
                      2. 6.02 kJ
                      3. 40.5 kJ
                      4. 62.3 kJ
                      5. 21.25 kJ
                      6. b
                      7. \(\Delta H*{vap}=\Delta H_f[H_2O(g)]-\Delta H_f[H_2O(l)]=-245.5-(-286)=40.5\,kJ\).
                      Q1.
                      Which of the following relations is correct?
                      📅IOM 2007
                      Q2.
                      Gibbs free energy (G), enthalpy (H) and entropy (S) are related by
                      📅IOM 2005•MOE 2009
                      Q3.
                      Decrease in the free energy of a reacting system indicates the reaction to be
                      Q4.
                      According to the first law of thermodynamics
                      📅MOE 09
                      Q5.
                      According to ΔG = ΔH - TΔS, spontaneity occurs when ΔG is
                      📅IOM 2008•BPKIHS
                      Q6.
                      The sum of internal energy and pressure-volume energy is
                      📅BPKIHS 2006
                      Q7.
                      In endothermic reactions, the reactants
                      Q8.
                      For the reaction Fe₂O₃ + 3CO → 2Fe + 3CO₂, which relation is correct?
                      📅BPKIHS
                      Q9.
                      PV = nRT is applicable to
                      📅MOE 2062
                      Q10.
                      When liquid boils, there is increase in
                      📅BPKIHS
                      Q11.
                      Which can be converted to useful work?
                      📅BPKIHS 2002
                      Q12.
                      For the process: Dry ice → CO₂(g)
                      📅Bangladesh 2008
                      Q13.
                      H, E, P and V are related as