Entropy: Screencasts

Introduces the second law of thermodynamics and describes some reversible and irreversible processes.

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Derives equations to calculate entropy changes for an ideal gas as temperature and pressure change.

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Derives equations to calculate entropy changes for liquids and solids and for phase changes.

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Optional screencast: How to Calculate Entropy Changes: Mixing Ideal Gases

Another optional screencast discusses continuous cycles and entropy.

Important Equations:

Definition of entropy change:

$\Delta S = \int \frac {dQ_{rev}}{T}$

only true for reversible heat transfer $$(Q)$$and must use absolute temperature, $$T$$

Entropy change for a phase change:

$\Delta S = \frac {\Delta H}{T}$

where $$\Delta H$$ is the enthalpy change for the phase change and $$T$$ is the absolute temperature at which the phase change take place.

Entropy change (per mole of mixture) of mixing ideal gases at constant temperature and constant pressure:

$\Delta S = -R \sum y_ilny_i$

where $$R$$ is the ideal gas constant, and $$y_i$$ is the mole fraction of component $$i$$ in the gas phase.

Entropy change per mole for an ideal gas where initial state s $$P_1, V_1, T_1$$ and the final state $$P_2, V_2, T_2$$:

$\Delta S = C_P \, ln\left(\frac{T_2}{T_1}\right) – R\,ln\left(\frac{P_2}{P_1}\right)$

$\Delta S = C_V \, ln\left(\frac{T_2}{T_1}\right) + R\,ln\left(\frac{V_2}{V_1}\right)$

where the heat capacities $$(C_P, C_V)$$ are constant.

Entropy change for liquids or solids when temperature increases from $$T_1$$ to $$T_2$$ :

$\Delta S = C_P \, ln\left(\frac{T_2}{T_1}\right)$

where $$C_P$$ is the heat capacity, which is assumed constant for a liquid or solid. Absolute temperature must be used in this equation. At most pressures, the entropy of liquids or solids does not change significantly when the pressure changes.