Thermodynamics - Entropy and Heat Capacities

Flashcards covering molar heat capacities, Poisson's ratio for various gases, and entropy change formulas for phase transitions and gas processes.

Monoatomic Gas ($He, Ne, Ar$)

$C_V = \frac{3}{2}R$, $C_P = \frac{5}{2}R$, and Poison's Ratio (r) = $1.67$

Diatomic Gas ($O_2, N_2, H_2$)

$C_V = \frac{5}{2}R$, $C_P = \frac{7}{2}R$, and Poison's Ratio (r) = $1.40$

Linear Polyatomic Gas ($CO_2, HCN$)

$C_V = \frac{5}{2}R$, $C_P = \frac{7}{2}R$, and Poison's Ratio (r) = $1.40$

Non-linear Polyatomic Gas ($CH_4, H_2O, NH_3$)

$C_V = 3R$, $C_P = 4R$, and Poison's Ratio (r) = $1.33$

Reaction: $2A(g) \rightarrow A_2(g)$ (Bond Formation)

The enthalpy change is negative ($\Delta H < 0$) and the entropy change is negative ($\Delta S < 0$)

Entropy Change of System ($\Delta S_{sys}$) General Formula

$$\Delta S_{sys} = n C_V \ln\left(\frac{T_2}{T_1}\right) + n R \ln\left(\frac{V_2}{V_1}\right)$$

Entropy of Fusion ($\Delta S_{fus}$)

$\Delta S_{fus} = \frac{\Delta H_{fus}}{T_{mp}}$ (per mol)

Entropy of Vaporization ($\Delta S_{vap}$)

$\Delta S_{vap} = \frac{\Delta H_{vap}}{T_{bp}}$ (per mol)

Entropy of Sublimation ($\Delta S_{sub}$)

$\Delta S_{sub} = \frac{\Delta H_{sub}}{T_{sub}}$ (per mol)

$\Delta S_{sys}$ for Isothermal Reversible Process

$$\Delta S_{sys} = n R \ln\left(\frac{V_2}{V_1}\right) = n R \ln\left(\frac{P_1}{P_2}\right)$$

Universe Entropy ($\Delta S_{univ}$) for Reversible Process

$\Delta S_{univ} = 0$ because $\Delta S_{sys} = -\Delta S_{surr}$

Entropy Change for Reversible Adiabatic Process

$\Delta S_{sys} = 0$ and $\Delta S_{surr} = 0$, hence $\Delta S_{univ} = 0$

Entropy Change for Irreversible Adiabatic Process

$\Delta S_{sys} > 0$ and $\Delta S_{surr} = 0$, hence $\Delta S_{univ} > 0$

$\Delta S_{surr}$ in Irreversible Isothermal Expansion

$$\Delta S_{surr} = \frac{-P_{ext}(V_2 - V_1)}{T}$$

Spontaneous Process Criterion

A process is spontaneous when the total entropy change of the universe is positive ($\Delta S_{univ} > 0$)