Chemical thermodynamics formula - Practice Questions & MCQ

Ideal gas

Gas equation: $p V=n R T=N k_B T$
Internal energy. $U=n C_V T$

Speed of molecule: $v=\sqrt{\frac{3 k T}{m}}$

Capacities: $C_P=C_V+R$, Ratio: $\gamma=\frac{C_P}{C_V}$

Degree of Freedom

Monoatomic: $(\mathrm{f}=3)$

$
\begin{aligned}
& \mathrm{C}_{\mathrm{V}}=\frac{3}{2} \mathrm{R} \\
& \mathrm{C}_{\mathrm{p}}=\mathrm{R}\left(\frac{3}{2}+1\right)=\frac{5 \mathrm{R}}{2}
\end{aligned}
$
 

Diatomic: $(\mathrm{f}=5)$

$
\begin{aligned}
& \mathrm{C}_{\mathrm{V}}=\frac{5}{2} \mathrm{R} \\
& \mathrm{C}_{\mathrm{p}}=\mathrm{R}\left(\frac{5}{2}+1\right)=\frac{7 \mathrm{R}}{2}
\end{aligned}
$
 

Polyatomic: $(\mathrm{f}=6)$

$
\begin{aligned}
& \mathrm{C}_{\mathrm{V}}=\frac{6}{2} \mathrm{R} \\
& \mathrm{C}_{\mathrm{p}}=\mathrm{R}\left(\frac{6}{2}+1\right)=4 \mathrm{R}
\end{aligned}
$
 

Thermodynamic process

First law: $\Delta U=Q-W$

Work: $W_{A \rightarrow B}=\int_A^B p d V$

Entropy: $\Delta S=\int_A^B \frac{d Q}{T}$

Special processes

$
\begin{array}{|c|c|c|c|c|}
\hline & \text { Isochoric } & \text { Isobaric } & \text { Isothermal } & \text { Adiabatic } \\
\hline \text { Definition } & \Delta V=0 & \Delta P=0 & \Delta T=0 & Q=0 \\
\text { Ideal gas } & p V=n R T & p V=n R T & p V=n R T & p V=n R T, p V^\gamma=\text { const } \\
\text { Work } & W=0 & W=p\left(V_2-V_1\right) & W=n R T \ln \frac{V_2}{V_1} & W=n C_V\left(T_1-T_2\right)=\frac{1}{1-\gamma}\left(p_2 V_2-p_1 V_1\right) \\
\text { Heat } & Q=n C_V \Delta T & Q=n C_P \Delta T & Q=W & Q=0 \\
\text { Internal E } & \Delta U=Q & \Delta U=Q-W & \Delta U=0 & \Delta U=-W \\
\text { Entropy } & \Delta S=n C_V \ln \frac{T_2}{T_1} & \Delta S=n C_P \ln \frac{T_2}{T_1} & \Delta S=n R \ln \frac{V_2}{V_1} & \Delta S=0 \\
\hline
\end{array}
$

Constants

Gas: $R=8.31 \mathrm{~J} / \mathrm{K} . \mathrm{mol}$
Boltzmann: $k_B=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$
Avogadro: $N_A=6.02 \times 10^{23} / \mathrm{mol}$

Stefan-Boltzmann: $\sigma=5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{~K}^4$

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