3.6
Absolute Entropies and the Third Law of Thermodynamics
Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number…
Entropy is unique among state functions because it possesses a measurable, absolute value.
We define this value through the Boltzmann relationship: the absolute entropy is proportional to the natural logarithm of the number of possible microstates, or particle arrangements.
When a gas-filled container expands, a larger volume allows for more closely spaced energy levels, which become populated even at the same temperature. This increases the total number of accessible microstates, increasing the system’s entropy.
At absolute zero, all thermal motion ceases. In a perfectly ordered crystal, the atoms align in a singular, unique arrangement. Because there is only one possible microstate, the natural log of one is zero, resulting in zero entropy. This is the Third Law of Thermodynamics.
However, the "perfect crystal" is an ideal. In reality, residual entropy may persist even at zero kelvin. This occurs when molecules can be "frozen" in different orientations, like carbon monoxide molecules facing random directions. This persistent disorder means the entropy remains slightly above zero.
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Q1: What is the Boltzmann relationship and how does it define absolute entropy?
The Boltzmann relationship defines absolute entropy as proportional to the natural logarithm of the number of possible microstates, or particle arrangements, in a system. This makes entropy unique among state functions because it possesses a measurable, absolute value. The more microstates available to a system, the higher its entropy.
Q2: How does container expansion affect the entropy of a gas?
When a gas-filled container expands, the volume increases, allowing energy levels to become more closely spaced and more densely populated. This increases the total number of accessible microstates at the same temperature, thereby increasing the system's entropy. Larger volume directly enables greater molecular disorder.
Q3: What does the Third Law of Thermodynamics state about entropy at absolute zero?
The Third Law of Thermodynamics states that at absolute zero temperature, all thermal motion ceases. In a perfectly ordered crystal, atoms align in a singular, unique arrangement with only one possible microstate. Since the natural logarithm of one equals zero, the entropy of a perfect crystal is zero at absolute zero.
Q4: Why does residual entropy sometimes persist at absolute zero?
Residual entropy persists at absolute zero when molecules become frozen in different orientations rather than a single perfect arrangement. For example, carbon monoxide molecules may face random directions even at zero kelvin. This persistent molecular disorder means entropy remains slightly above zero despite the absence of thermal motion.
Q5: What is the difference between absolute entropy and Third-Law entropy?
Absolute entropy is the measurable entropy value of any system based on the Boltzmann relationship. Third-Law entropy, denoted S°(T), is calculated assuming the entropy of a perfectly ordered crystalline substance equals zero at absolute zero. Third-Law entropies account for residual disorder and are reported relative to this reference point.
Q6: How does heat supply affect the number of microstates in a system?
When heat is supplied to a system, it propels molecules into higher energy states, increasing the number of available energy levels and accessible microstates. This expansion of available molecular arrangements directly increases the system's entropy. Heat input enables greater disorder and more possible particle configurations.
Q7: Why is entropy unique compared to other state functions?
Entropy stands alone among state functions as the only one whose absolute values can be determined through the Boltzmann relationship. Other state functions lack this measurable absolute reference point. This uniqueness allows scientists to calculate absolute entropy values directly from the number of possible microstates.