Why entropy is an extensive quantity ?

• abcdefg10645
In summary: Thanks a lot ! :)Using the integral to calculate the (delta)S "OF A SYSTEM" is to calculate the difference of entropy for a particular process. I want to ask why , for different systems , it can also be added ?How's that?
abcdefg10645
Why entropy is an extensive quantity ?

Hi.
Entropy increase by volume. Gas of 2 m^3 have double entropy than gas of 1 m^3 in the same temperature and pressure.
Regards.

sweet springs said:
Hi.
Entropy increase by volume. Gas of 2 m^3 have double entropy than gas of 1 m^3 in the same temperature and pressure.
Regards.

But how do you know that "Entropy increase by volume. "

Let me restate my question :

How can ew know that entropy is an extensive quantity by its definition

dS=$$\int(dQ/T)$$

Hi.
First law of thermodynamics, about the conservation of energy: δQ=dU - dW =dU - pdV
δQ is extensive because dU and pdV are extenxive. δQ/T and ∫δQ/T are also extensive.
Regards.

sweet springs said:
Hi.
First law of thermodynamics, about the conservation of energy: δQ=dU - dW =dU - pdV
δQ is extensive because dU and pdV are extenxive. δQ/T and ∫δQ/T are also extensive.
Regards.

But for different systems , their temperature T may not be the same !

First Law sates that deltaQ=dU+deltaW

We can only infer that deltaQ is additive !

Thanks

Hi.

abcdefg10645 said:
But for different systems , their temperature T may not be the same !
First Law sates that deltaQ=dU+deltaW
We can only infer that deltaQ is additive !

Thanks for correcting my sign mistake of deltaW.
You are right. Additive is the essence of extensive quantity. For isolated two different systems
S1 = ∫dQ1/T1, S2 = ∫dQ2/T2 and the entropy of total system is S = S1 + S2.
Regards.

sweet springs said:
Hi.

Thanks for correcting my sign mistake of deltaW.
You are right. Additive is the essence of extensive quantity. For isolated two different systems
S1 = ∫dQ1/T1, S2 = ∫dQ2/T2 and the entropy of total system is S = S1 + S2.
Regards.

Ha ha~never mind ~I believe that were just some typos

But , I cannot understand why entropy is additive ?

Hi.
Definition ∫　δQ/T is already addition of　δQ/T , isn't it ?
Regards.

sweet springs said:
Hi.
Definition ∫　δQ/T is already addition of　δQ/T , isn't it ?
Regards.

Using the integral to calculate the (delta)S "OF A SYSTEM" is to calculate the difference of entropy for a particular process , I want to ask why , for different systems , it can also be added ?

Hi. How's that?

1 m^3 of liquid water of the room temperature and in standard pressure has entropy say S.
Let us remove half of water. Do you agree that the left water has entropy S/2 ?

We will bring removed water into another isolated room of the same temperature and pressure.
Do you agree that brought water has entropy S/2?

Water in the first room and water in the second room are different systems.
Do you agree that the integrated system of the two has entropy S?

In room 1 we increase the temperature then the entropy of water becomes S'/2
Do you agree that the integrated system of the two has entropy S/2 + S'/2 ?
Change of entropy ∫δQ/T for room 1 system is regarded as change of entropy in the integrated system, isn't it?

Regards.

Last edited:
Thank u ~

I can now fully understand the reason why entropy is additive by ur explaining steps by steps !

1. Why is entropy considered an extensive quantity?

Entropy is considered an extensive quantity because it depends on the size or amount of the system. This means that as the system grows, the entropy also increases.

2. How is the extensive property of entropy related to its definition?

The extensive property of entropy is related to its definition because it is a measure of the disorder or randomness of a system. As the size of the system increases, the number of possible arrangements or microstates also increases, resulting in a higher level of disorder and therefore a higher entropy.

3. Can you give an example of an extensive quantity other than entropy?

An example of an extensive quantity other than entropy is mass. The mass of a system increases as more matter is added to it, just as the entropy of a system increases as it becomes larger.

4. What is the significance of entropy being an extensive quantity in thermodynamics?

The extensive property of entropy in thermodynamics is significant because it allows for the calculation of the total entropy of a system by adding the individual entropies of its components. This is important in understanding the overall behavior of a system and predicting changes in entropy during processes.

5. How does the extensive property of entropy affect the second law of thermodynamics?

The extensive property of entropy is directly related to the second law of thermodynamics, which states that the total entropy of an isolated system always increases over time. This is because as the system grows, the number of possible microstates also increases, leading to a higher overall entropy. Therefore, the extensive property of entropy supports the second law of thermodynamics.

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