7: Calculation of Entropy and the Third Law of Thermodynamics
- Page ID
- 414058
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The Second Law can be used to infer the spontaneity of a process, as long as the entropy of the universe is considered. To do so, we need to remind ourselves that the universe can be divided into a system and its surroundings (environment). When we calculate the entropy of the universe as an indicator of the spontaneity of a process, we need to always consider changes in entropy in both the system (sys) and its surroundings (surr):
\[ \Delta S^{\mathrm{universe}} = \Delta S^{\mathrm{sys}} + \Delta S^{\mathrm{surr}}, \nonumber \]
or, in differential form:
\[ d S^{\mathrm{universe}} = d S^{\mathrm{sys}} + d S^{\mathrm{surr}}, \nonumber \]
- 7.1: Calculation of ΔSsys
- In general ΔSsys can be calculated using either its Definition: Entropy, or its differential formula, Equation 6.1.5. In practice, it is always convenient to keep in mind that entropy is a state function, and as such it does not depend on the path.
- 7.2: Calculation of ΔSsurr
- While the entropy of the system can be broken down into simple cases and calculated using the formulas introduced above, the entropy of the surroundings does not require such a complicated treatment, and it can always be calculated as:
- 7.3: Clausius Theorem
- By replacing Equation 7.2.2 into 7.2 we can write the differential change in the entropy of the system as:
- 7.4: The Third Law of Thermodynamics
- The Third Law of Thermodynamics sets an unambiguous zero of the entropy scale, similar to what happens with absolute zero in the temperature scale. The absolute value of the entropy of every substance can then be calculated in reference to this unambiguous zero. As such, absolute entropies are always positive. This is in stark contrast to what happened for the enthalpy.