Important Thermodynamics Formulas for JEE and NEET

Thermodynamic processes :

• Isothermal process: T = constant
  dT = 0
  ΔT = 0
• Isochoric process: V = constant
  dV = 0
  ΔV = 0
• Isobaric process: P = constant
  dP = 0
  ΔP = 0
• Adiabatic process: q = 0
  or heat exchange with the surrounding = O(zero)

IUPAC Sign convention about Heat and Work :
Work done on the system = Positive
Work done by the system = Negative 

1^st Law of Thermodynamics
ΔU = (U₂ - U₁) = q + w

Law of equipartion of energy :
 (only for ideal gas)

where f= degrees of freedom for that gas. (Translational + Rotational)
f = 3 formonoatomic
= 5 for diatomic or linear polyatmic
= 6 for non - linear polyatmic

Calculation of heat (q): 
Total heat capacity:

Molar heat capacity :

Specific heat capacity (s):

WORK DONE (w) :
Isothermal Reversible expansion/compression of an ideal gas :
W = - nRT In (V_f/V_i)

Reversible and irreversible isochoric processes.
Since dV = 0
So dW = - P_ext . dV = 0.

Reversible isobaric process:
W = P (V_f - V_i)
Adiabatic reversible expansion :

Reversible Work:

Irreversible Work :

Free expansion - Always going to be irrerversible and since P_ext = 0
so dW = -P_ext..dV = 0
If no. heat is supplied q = 0
then ΔE = 0 so ΔT = 0.

Application of 1st Law :
ΔU = ΔQ + ΔW ⇒ ΔW = -P ΔV
∴ ΔU = ΔQ -PΔV

Constant volume process
Heat given at constant volume = change in internal energy
∴du = (dq)_v
du = nC_vdT

Constant pressure process:
H ≡ Enthalpy (state function and extensive property)
H = U + PV

⇒ C_p - C_v = R (only for ideal gas)

Second Law Of Thermodynamics :
 fo r a spontaneous process.

Entropy (S):

Entropy calculation for an ideal gas undergoin a process :

 (only for an ideal gas)

Third Law Of Thermodynamics :
The entropy of perfect crystals of all pure elements & compounds is zero at the absolute zero of temperature.

Gibb’s free energy (G) : (State function and an extensive property)

Criteria of spontaneity:
(i) If ΔG_system is (-ve) < 0 ⇒ process is spontaneous
(ii) If ΔG_system is > 0 ⇒ process is non spontaneous
(iii) lf ΔG_system  = 0 = 3 system is at equilibrium.

Physical interpretation of ΔG :
 The maximum amount of non-expansional (compression) work which can be performed.

Standard Free Energy Change (ΔG°) :
1. ΔG° = -2.303 RTIog₁₀K
2. At equilibrium ΔG = 0.
3. The decrease in free energy (-ΔG) is given as :

4. for elemental state = 0

5.

Thermochemistry:
Change in standard enthalpy

= heat added at constant pressure. =  C_PΔT.
If H_products > H_reactants

• Reaction should be end other micas we have to give extra heat to reactants to get these converted into products and if
  H_products > H_reactants
• <sub>Reaction will be exothermic as extra heat content of reactants will be released during the reaction. Enthalpy change of a reaction :
  
  
  = positive - endothermic
  = negative - exothermic</sub>

_{Temperature Dependence Of ΔH : (Kirchoff's equation):
For a constant volume reaction}

where ΔC_P = C_p (products) - C_p (reactants).
For a constant volume reaction

Enthalpy of Reaction from Enthalpies of Formation :
The enthalpy of reaction can be calculated by
  is the stoichiometric coefficient.

Estimation of Enthalpy of a reaction from bond Enthalpies :

Resonance Energy: