# 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}
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}

This was the list of All Formulas of Thermodynamics Chemistry Class 11. You can get complete formula bank here.