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.