How to calculate entropy for a system

In summary, entropy can be measured accurately using the thermodynamic definition S = \int_{0}^T \frac{dQ}{T} + S_0, where S0 is the entropy at absolute zero. However, calculating the entropy for a complicated system can be difficult as it requires knowledge of the heat capacity at various temperatures.
  • #1
CraigH
222
1
How can you acuratley measure this? I can't see how you can give randomness a number? I've seen in some places that S = ln(the number of possible arangments) Is this true in all cases? But how can you measure the number of possible arangements?, it seems imposible to calculate the entropy for a complicated system.
Thanks
 
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  • #2
CraigH said:
How can you acuratley measure this? I can't see how you can give randomness a number? I've seen in some places that S = ln(the number of possible arangments) Is this true in all cases? But how can you measure the number of possible arangements?, it seems impossible to calculate the entropy for a complicated system.
Thanks
The thermodynamic definition of entropy S at a temperature T is:

[itex]S = \int_{0}^T dS + S_0 = \int_{0}^T \frac{dQ}{T} + S_0 [/itex]

where S0 is the entropy at absolute zero which is not really defined but you can take it to be 0. Strictly speaking, it is only zero for molecular structures that can have only one microstate at absolute zero.

In order to calculate this integral, you just need to know the heat capacity of the substance as a function of temperature.

AM
 
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1. How do you define entropy?

Entropy is a measure of the disorder or randomness in a system. It is a thermodynamic property that quantifies the amount of energy in a system that is unavailable for work.

2. What is the formula for calculating entropy?

The formula for calculating entropy is S = k ln W, where S is the entropy, k is the Boltzmann constant, and W is the number of microstates available to the system at a given macrostate.

3. How do you determine the number of microstates in a system?

The number of microstates in a system can be determined by considering the different ways in which the particles or components of the system can be arranged while still maintaining the same overall energy and macrostate.

4. Does the entropy of a system always increase?

According to the second law of thermodynamics, the total entropy of a closed system (one that does not exchange matter or energy with its surroundings) will always increase over time. However, in certain circumstances, the entropy of a specific part of the system may decrease.

5. How does entropy relate to the concept of disorder?

The higher the entropy of a system, the more disordered or random it is. This is because as entropy increases, there are more possible arrangements that the system's components can take on, making it more difficult to predict their exact positions or states.

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