# [Thermal] Is it possible that increases of moles decrease entropy?

• coocoo
In summary, the conversation discusses the entropy of a system at a given temperature, volume, and number of moles. The formula for calculating entropy is given, with specific heat and a constant also included. It is noted that increasing volume and temperature will increase entropy, but keeping other variables constant may result in a maximum value for entropy. The conversation also mentions the possibility of uploading a photo file and expresses confusion about the relationship between moles and entropy.
coocoo
From Statsitical And Thermal Physics (Reif. international edition 1985)

160 page. (5.4.4)

S(T,V;√) = √[∫{cv(T)/T}dT` + Rln(V) - Rln(√) + constant]

(integral is from T0 to T , cv is specific heat)

This is a entropy of system for temperature 'T' , Volume 'V' , Moles '√' <-- this is mu

as you see, by increasing volume and temperature, entropy increases (trivial)

but by fixing other variables except for moles,

there is some extreme max value.

i.e. entropy gets lowered by incresing moles from some point.

ps. Is there any way that I can upload my photo file in my computer?

I expected increases of moles makes entropy higher.

What is the problem??

## 1. Is it possible for an increase in moles to decrease entropy?

Yes, it is possible for an increase in moles to decrease entropy. Entropy is a measure of the disorder or randomness in a system, and an increase in the number of moles can lead to a decrease in order and therefore a decrease in entropy.

## 2. How does increasing moles affect entropy?

Increasing moles can decrease entropy by increasing disorder and randomness in a system. This can happen, for example, when a gas expands into a larger volume, increasing the number of moles and decreasing the overall order of the system.

## 3. Can increasing moles lead to a decrease in temperature?

Yes, increasing moles can lead to a decrease in temperature. This is known as the Joule-Thomson effect, where a gas will cool down when it expands into a lower pressure environment. This decrease in temperature is a result of the decrease in order and increase in randomness.

## 4. What is the relationship between moles and entropy?

The relationship between moles and entropy is complex and depends on the specific system. In general, an increase in moles can lead to a decrease in entropy by increasing disorder and randomness. However, there are also cases where an increase in moles can lead to an increase in entropy, such as in a mixture of gases where the different gases can have different entropy values.

## 5. Can entropy ever decrease?

Yes, entropy can decrease in a process known as negative entropy or negentropy. This occurs when a system becomes more ordered and less random, such as in the formation of crystals. However, this decrease in entropy is often accompanied by an increase in entropy in the surrounding system, maintaining the overall increase of entropy in the universe as described by the second law of thermodynamics.

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