Entropy Change in Free Expansion: Why △S=ncᵥln(T_f/T_i)+nRln(V_f/V_i)?

In summary: Yes, the scheme in Posts #2 and #3 must yield the same change in entropy as the actual irreversible process. However, the two schemes need not be identical.
  • #1
spideyjj
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In a free expansion, I know that we cannot use the equation dS=dQ/T...(1). Instead we use dS>dQ/T...(2).

The question is that why we can use △S=ncᵥln(T_f/T_i)+nRln(V_f/V_i) , which is derived from the equation(1), to calculate the entropy change? Shouldn’t it be a inequality too?
 
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  • #2
Entropy is a state function and doesn’t depend on the path by which the system arrived at its present state. The entropy change on going from an initial state to a final state is thus independent of how the final state is arrived at. To calculate the entropy change dS for an irreversible process, one generally designs a reversible process - linking the same two endpoints - by means of which dS can be calculated using dS = δQrev/T.
 
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  • #3
Lord Jestocost said:
Entropy is a state function and doesn’t depend on the path by which the system arrived at its present state. The entropy change on going from an initial state to a final state is thus independent of how the final state is arrived at. To calculate the entropy change dS for an irreversible process, one generally designs a reversible process - linking the same two endpoints - by means of which dS can be calculated using dS = δQrev/T.
I would add that the designed reversible process does not need to bear any resemblance whatsoever to the actual irreversible process, except insofar as matching the initial and final thermodynamic equilibrium states.
 
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  • #4
Don't the beginning and ending states have to be equilibrium states for the scheme described in Posts #2 and #3 to be valid ways of finding the change in entropy?
 
  • #5
Mister T said:
Don't the beginning and ending states have to be equilibrium states for the scheme described in Posts #2 and #3 to be valid ways of finding the change in entropy?
Isn't that what I said?
 

Related to Entropy Change in Free Expansion: Why △S=ncᵥln(T_f/T_i)+nRln(V_f/V_i)?

1. What is entropy change in free expansion?

Entropy change in free expansion refers to the change in the measure of disorder or randomness in a system when it undergoes a process of expansion without any external work being done on it. This process is also known as irreversible or adiabatic expansion.

2. Why is △S=ncᵥln(T_f/T_i)+nRln(V_f/V_i) the formula for calculating entropy change in free expansion?

This formula is derived from the second law of thermodynamics, which states that the total entropy of an isolated system will always increase over time. In the case of free expansion, there is no work being done on the system, so the change in entropy is solely dependent on the change in temperature and volume of the system.

3. What does "ncᵥ" and "nR" represent in the formula for entropy change in free expansion?

ncᵥ represents the number of moles of the gas undergoing expansion multiplied by the heat capacity at constant volume. nR represents the number of moles of the gas multiplied by the universal gas constant. These values are used to account for the effects of temperature and volume on entropy change.

4. Is entropy change always positive in free expansion?

Yes, entropy change is always positive in free expansion because the gas molecules in the system become more randomly distributed, leading to an increase in disorder. This is in line with the second law of thermodynamics, which states that the total entropy of an isolated system will always increase over time.

5. How does the temperature and volume ratio affect the entropy change in free expansion?

The temperature and volume ratio, represented by (T_f/T_i) and (V_f/V_i) in the formula, have a direct relationship with the entropy change. As the temperature ratio increases, the entropy change also increases. Similarly, as the volume ratio increases, the entropy change also increases. This is because both temperature and volume play a role in the measure of disorder or randomness in a system.

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