7: Calculation of Entropy and the Third Law of Thermodynamics

The Live Textbook of Physical Chemistry I · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under CC BY-SA 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    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.

    This page titled 7: Calculation of Entropy and the Third Law of Thermodynamics was last modified on Thu, 24 Nov 2022 19:18:27 GMT and is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Roberto Peverati via source content that was edited to the style and standards of the LibreTexts platform.