Consider a system that consists of two standard playing dice, with the state of the system defined by the sum of the values shown on the top faces. (f) Calculate the absolute entropy of the two-dice system.

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Identify the possible outcomes for the sum of the top faces when two dice are rolled. The sums can range from 2 (1+1) to 12 (6+6).

Calculate the number of microstates (Ω) for each macrostate (sum). For example, the sum of 2 can only occur in one way (1+1), while the sum of 7 can occur in six ways (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).

Sum up all the microstates for each possible sum to find the total number of microstates for the system.

Use the formula for absolute entropy, S = k * ln(Ω), where k is the Boltzmann constant and Ω is the total number of microstates.

Substitute the total number of microstates into the entropy formula to calculate the absolute entropy of the system.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state. Higher entropy indicates a greater number of possible arrangements, reflecting a more disordered state. In the context of dice, the entropy can be calculated based on the number of possible outcomes for the sums of the dice.

Statistical Mechanics

Statistical mechanics is a branch of physics that connects the microscopic properties of individual atoms and molecules to the macroscopic properties of materials. It provides the framework for calculating thermodynamic quantities, such as entropy, by considering the probabilities of different microstates. For the two-dice system, statistical mechanics helps determine the likelihood of each possible sum and thus the overall entropy of the system.

Microstates and Macrostates

In statistical mechanics, a microstate refers to a specific detailed configuration of a system, while a macrostate is defined by macroscopic properties like temperature and pressure. The relationship between microstates and macrostates is crucial for calculating entropy, as the entropy of a macrostate is related to the number of microstates that correspond to it. For the two-dice system, each unique sum represents a macrostate, with multiple microstates contributing to that sum.

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