All Formulas of Thermodynamics Chemistry Class 11, JEE, NEET

Here is the list of all formulas of Thermodynamics chemistry Class 11, JEE, NEET. Please go through all the formulas below.

All Formulas of Thermodynamics Chemistry Class 11

Thermodynamic processes:
- Isothemal process:
  $\quad T =$ constant$ $\begin{array}{l} dT =0 \\ \Delta T =0 \end{array}
- Isochoric process:
  $V =$ constant$ $\begin{array}{l} d V=0 \\ \Delta V=0 \end{array}
- Isobaric process:
  $P =$ constant$ $\begin{array}{l} dP =0 \\ \Delta P =0 \end{array}
- Adiabatic process:
  q = 0
  or heat exchange with the surrounding $=0$ (zero)
IUPAC Sign convention about Heat and Work :
Work done on the system = Positive Work done by the system = Negative
$1^{\text {st }}$ Law of Thermodynamics
$$ \Delta U=\left(U_{2}-U_{1}\right)=q+w $$
Law of equipartion of energy:
$$ U =\frac{ f }{2} nRT \quad \text { (only for ideal gas) }$$
$$\Delta E =\frac{ f }{2} nR (\Delta T )$$
where $f=$ degrees of freedom for that gas. (Translational + Rotational)
$f=3 \quad$ for monoatomic
$f=5 \quad$ for diatomic or linear polyatmic
$f=6 \quad$ for non – linear polyatmic
Calculation of heat (q) :
- Total heat capacity:
  $C _{ T }=\frac{\Delta q }{\Delta T }=\frac{ dq }{ dT }= J /{ }^{\circ} C$
- Molar heat capacity:
  $C =\frac{\Delta q }{ n \Delta T }=\frac{ dq }{ ndT }= J mole ^{-1} K ^{-1}$
  $C _{ P }=\frac{\gamma R }{\gamma-1}$
  $C _{ v }=\frac{ R }{\gamma-1}$
- Specific heat capacity (s) :
  $S=\frac{\Delta q}{m \Delta T}=\frac{d q}{m d T}=J g m^{-1} K^{-1}$
WORK DONE (w) :
- Isothermal Reversible expansion/compression of an ideal gas :
  $$W =- nRT \ln \left( V _{ f } / V _{ i }\right)$$
- Reversible and irreversible isochoric processes
  since $\quad d V=0$
  So $\quad d W=-P_{\text {ext }} \cdot d V=0$
- Reversible isobaric process:
  $$W=P\left(V_{f}-V_{p}\right)$$
- Adiabatic reversible expansion :
  $\quad T _{2} V _{2}^{\gamma-1}= T _{1} V _{1}^{\gamma-1}$
- Reversible Work:
  $$W =\frac{P_{2} V_{2}-P_{1} V_{1}}{\gamma-1}=\frac{\operatorname{nR}\left(T_{2}-T_{1}\right)}{\gamma-1}$$
- Irreversible Work :
  $$W =\frac{P_{2} V_{2}-P_{1} V_{1}}{\gamma-1}=\frac{n R\left(T_{2}-T_{1}\right)}{\gamma-1} n C_{v}\left(T_{2}-T_{1}\right)=-P_{e x t}\left(V_{2}-V_{1}\right)$$ and use $$\frac{P_{1} V_{1}}{T_{1}}=\frac{P_{2} V_{2}}{T_{2}}$$
Free expansion – Always going to be irrerversible and since $P_{\text {ext }}=0$
so $\quad d W=-P_{\text {ext }} \cdot d V=0$
If no. heat is supplied $q =0$ then $\Delta E =0$ $\begin{array}{ll}\text { S0 } & \Delta T =0\end{array}$
Application of Ist Law :
$$\begin{aligned}
\Delta U =\Delta Q +\Delta W & \Rightarrow \quad \Delta W =- P \Delta V \\
\therefore U =\Delta Q – P \Delta V
\end{aligned}$$
Constant volume process
Heat given at constant volume = change in internal energy $\therefore du =( dq )_{ v }$
$du = nC _{ v } d T$
$C _{ v }=\frac{1}{ n } \cdot \frac{ du }{ dT }=\frac{ f }{2} R$
Constant pressure process:
$H \equiv$ Enthalpy (state function and extensive property)
$$H=U+P V$$
$\Rightarrow C_{0}-C_{y}=R$ (only for ideal gas)
Second Law Of Thermodynamics:
$\Delta S_{\text {unverse }}=\Delta S_{\text {system }}+\Delta S_{\text {surrounding }}>0$ for a spontaneous process.
Entropy (S):
$$\Delta S_{\text {system }}=\int_{A}^{B} \frac{d q_{r e v}}{T}$$
Entropy calculation for an ideal gas undergoin a process:
State $A \quad \frac{\text { irr }}{\Delta s_{\text {irr }}}$
State $B$
$P _{1}, V _{1}, T _{1} \quad P _{2}, V _{2}, T _{2}$
$\Delta S_{\text {system }}=n c_{v} \ln \frac{T_{2}}{T_{1}}+n R \ln \frac{V_{2}}{V_{1}} \quad$ (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)
$$G _{\text {system }}= H _{\text {system }}- TS _{\text {system }}$$
Criteria of spontaneity:
(i) If $\Delta G_{\text {system }}$ is $(-v e)<0 \Rightarrow$ process is spontaneous
(ii) If $\Delta G_{\text {system }}$ is $>0$
$\Rightarrow$
process is non spontaneous
(iii) If $\Delta G_{\text {system }}=0$
$\Rightarrow$
system is at equilibrium.
Physical interpretation of $\Delta G$ :
$\rightarrow$ The maximum amount of non-expansional (compression) work which can be performed.
$$
\Delta G = d w _{\text {non-exp }}= dH – TdS
$$
Standard Free Energy Change $\left(\Delta G^{\circ}\right):$
- $\Delta G ^{\circ}=-2.303 RT \log _{10} K$
- At equilibrium $\Delta G =0$.
- The decrease in free energy $(-\Delta G )$ is given as:
  $$
  -\Delta G = W _{\text {net }}=2.303 nRT \log _{10} \frac{ V _{2}}{ V _{1}}
  $$
- $\Delta G _{ f }^{\circ}$ for elemental state $=0$
- $\Delta G _{ f }^{\circ}= G _{\text {products }}^{\circ}- G _{\text {Reactants }}^{\circ}$
Thermochemistry:
Change in standard enthalpy $\Delta H ^{\circ}= H _{ m , 2}^{0}- H _{ m , 1}^{0}$
$=$ heat added at constant pressure. $= C _{ p } \Delta T$
If $\quad H _{\text {products }}> H _{\text {reactants }}$
- Reaction should be endothermic as we have to give extra heat to reactants to get these converted into products and if $H _{\text {products }}< H _{\text {reactants }}$
- Reaction will be exothermic as extra heat content of reactants will be released during the reaction. Enthalpy change of a reaction :
  $$
  \Delta H _{\text {reaction }}= H _{\text {products }}- H _{\text {reactants }}
  $$
  $\Delta H _{\text {reactions }}^{\circ}= H _{\text {products }}^{\circ}- H _{\text {reactants }}^{\circ}$
  $\Delta H _{\text {reactions }}^{\circ}=$ positive $\quad-$ endothermic
  $\Delta H _{\text {reactions }}^{\circ}=$ negative exothermic
Temperature Dependence Of $\Delta H$ : (Kirchoff’s equation) :
For a constant volume reaction
$\Delta H _{2}^{\circ}=\Delta H _{1}^{\circ}+\Delta C _{ p }\left( T _{2}- T _{1}\right)$
where $\Delta C _{ p }= C _{ p }($ products $)- C _{ p }$ (reactants).
For a constant volume reaction
$\Delta E _{2}^{0}=\Delta E _{1}^{0}+\int \Delta C _{ V } \cdot d T$
Enthalpy of Reaction from Enthalpies of Formation :
The enthalpy of reaction can be calculated by
$\Delta H _{ r }^{\circ}=\Sigma v _{ B } \Delta H _{ f }^{\circ},_{\text {products }}-\Sigma v _{ B } \Delta H _{ f }^{\circ},$
reactants $\quad v _{ B }$ is the stoichiometric coefficient.
Estimation of Enthalpy of a reaction from bond Enthalpies:
Resonance Energy:
\begin{aligned}
\Delta H _{\text {resonance }}^{\circ} &=\Delta H ^{\circ}{ }_{ f , \text { experimental }}-\Delta H _{ f , \text { calclulated }}^{\circ} \\
&=\Delta H ^{\circ}{ }_{ c , \text { calclulated }}^{\circ}-\Delta H ^{\circ}{ }_{ c , \text { experimental }}
\end{aligned}