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

1. Mar 9, 2014

### 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??

2. Mar 9, 2014