THERMODYNAMICS

1. Mechanical Work
   W = - P_ext (ΔV) [during expansion]
2. First Law of Thermodynamics
   ΔE = q + W
   ΔE = q - PΔV
3. Adiabatic Change
   
4. Isochoric Change
   ΔV = 0
   W = PΔV = 0
   ΔE = q + W = q
5. Cyclic Change (reversible)
   ΔE = 0
   q = -W = PΔV
   q = -W_max = P∫dV
6. Isothermal reversible Expansion
   ΔH = ΔE = 0 (internal energy is a function of temperature)
   q = -W_max = 2.303 nRT log( V₂ / V₁) = 2.303 nRT log( P₁ / P₂)
   ΔH = ΔE + Δn_gRT
7. Joule - Thompson coefficient 
   
   (i) For cooling , u > 0 (-ve sign)
   (ii)For heating , u < 0 (+ve sign)
8. Second Law of Thermodynamics 
   Efficiency of the Carnot engine = η = 
   q₂ - q₁q₂
    = 
   T₂ - T₁T₂
    = 1 - 
   T₁T₂
   
   q₂ = heat absorbed by engine
   q₁ = heat lost to sink
9. Entropy Change 
   ΔS_total = ΔS_system + ΔS_surrounding
   ΔS_fusion = 
   ΔH_fusionT_fusion
    ; ΔS_vapour = 
   ΔH_vapourT_vapour
10. Gibb's Free Energy (G)
    ΔG = G₂ - G₁
    ΔG = ΔH - TΔS (Gibb's Helmholtz equation)
    ΔG < 0 (means spontaneous process)
    ΔG > 0 (means non-spontaneous process)
    ΔG = 0 (means system is at equilibrium)
11. Kirchoff's Equation
    
    ΔH₂ - ΔH₁T₂ - T₁
     = ΔC_p and 
    ΔE₂ - ΔE₁T₂ - T₁
     = ΔC_v
    where , ΔC_p = ∑C_p(products) - ∑C_p(reactants) and ΔC_v = ∑C_v(products) - ∑C_v(reactants)
12. Degree of Dissociation (x)
    x = 
    D - dd
     = 
    M_t - M_oM_o
    
    where , D = theoretical V.D. and d = observed V.D.
13. pH of a solution
    pH = -log[H₃O⁺]
    pOH = -log[OH^-]
    pH + pOH = pK_W = 14
14. Isothermal (reversible)
    ΔS = 2.303 nR log (V₂ / V₁)
    at constant pressure ,
    ΔS = 2.303 C_p log₁₀ (T₂ / T₁)
    For vaporization ,
    ΔS = 
    ΔH_vapT_bp
    
    ΔG^o = - nFE⁰_cell
15. Sign Convention
    
    • If work is done on the system , W is +ve.
    • If work is done by the system , W is -ve.
    • If heat is absorbed by the system , or ΔH is +ve.
    • If heat is given out by the system , q or ΔH is -ve.
    • If energy is absorbed by the system , i.e. internal energy increases , ΔE is +ve.
    • If energy is released i.e., internal energy of the system decreases , ΔE is -ve.
16. Heat Capacity
    (i) Heat capacity at constant volume , C_V = [ ∂E / ∂T ]_V
    (ii) Heat capacity at constant pressure , C_p = [ ∂H / ∂T ]_p
    For an ideal gas , C_p - C_v = R
17. Heat of Reaction
    ΔH = ∑ H_(p) - ∑ H_(R)
    For exothermic reaction : ∑ H_(p) < ∑ H_(R) (∴ Δ is -ve)
    For endothermic reaction : ∑ H_(p) > ∑ H_(R) (∴ Δ is +ve)
    Heat change at constant pressure = q_p = ΔH
    Heat change at constant volume = q_v = ΔH
    ΔH = ΔU + PΔV
    ΔH = ΔU + Δn_(g)RT
    If,
    Δn_(g) = 0 , ΔH = ΔU
    Δn_(g) > 0 , ΔH > ΔU
    Δn_(g) < 0 , ΔH < ΔU
18. Clausis - Clapeyron Equation
    
    where ΔH_v = molar heat of vapourisation
    
    • Calorific Value is the amount of heat evolved when one gram of fuel as food is burnt in the presence of air or excess of oxygen.
    • Joule's Relationship between work done (w) and heat produced (H)
      W α H or W = JH
      where J = mechanical equivalent of heat ; J = 4.184 JCal^-1
    • S₁ and S₂ are solubility at temperature T₁ and T₂ respectively