Solving Number of Molecules for Entropy of 1.181x10^-12 J/K

In summary, the conversation discusses the calculation of the number of molecules in a solid sample of a compound that can point in any two directions and have the same energy. Using the equation S = k*ln(W), where S is entropy, k is Boltzmann constant, and W is the number of microstates, the individual attempted to solve for W. However, the calculation was incorrect and it was determined that there are 2 microstates for 1 molecule and many more possible combinations for multiple molecules. The final step is to determine the number of molecules in the sample.
  • #1
samueltak
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Homework Statement


Suppose a compound could point in any two directions in the solid and still have the same energy. How many molecules would there be if the total entropy of a solid sample of this compound was 1.181x10^-12 J/K?

Homework Equations


My plan that failed -

S = k*ln(W),
where S is entropy
k is Boltzman constant = 1.38 x 10-23 (J/K) or equivalent to (Universal Gas Constant 8.314/Avogadro's number 6.02 x 1023 molecules/mol)
W is the number of microstates

The Attempt at a Solution


1.181x10^-12 J/K = (8.314/ x 6.02*1023)*(ln(2)), I put 2 in ln(2) because I thought the question stated the total microstates when it said "...point in any two directions".

I solved for x and got 3.242e13 which is wrong.
 
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  • #2


Welcome to Physics Forums.

It would be 2 microstates if there were just 1 molecule. With many molecules, there are many many possible combinations of their orientations.

Treat W as an unknown, and solve for it. Once you have W, the final step will be to figure out how many molecules.
 

Related to Solving Number of Molecules for Entropy of 1.181x10^-12 J/K

1. How do you calculate the number of molecules for a given entropy value?

The number of molecules can be calculated using the formula N = k * ΔS / ln(2), where N is the number of molecules, k is the Boltzmann constant (1.381x10^-23 J/K), and ΔS is the given entropy value (1.181x10^-12 J/K).

2. What is the significance of the entropy value 1.181x10^-12 J/K?

The entropy value of 1.181x10^-12 J/K represents the amount of disorder or randomness in a system. It is a measure of the number of microstates that a system can occupy at a given energy level. In other words, it quantifies the level of chaos or unpredictability in a system.

3. How does the number of molecules affect the entropy value?

The number of molecules directly influences the entropy value. As the number of molecules increases, the entropy also increases. This is because a larger number of molecules means a larger number of microstates, resulting in a higher level of disorder and subsequently, a higher entropy value.

4. What is the relationship between entropy and temperature?

Entropy and temperature have an inverse relationship. As temperature increases, the entropy also increases. This is because at higher temperatures, molecules have more energy and can move around more freely, resulting in a higher number of microstates and therefore, a higher entropy value.

5. How is the concept of entropy useful in scientific research?

The concept of entropy is used in various fields of science such as thermodynamics, chemistry, and biology. It helps in understanding the behavior of systems and predicting their changes over time. It also plays a crucial role in the design and optimization of processes and systems in engineering and technology.

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