# Entropy properties

1. Mar 23, 2013

### Guffie

hello,

i have been given two formulae for the entropy of an ideal gas undergoing a reversible process.

the correct expression is:

S = Nk(s0-ln$({\frac{N_0}{N}})^{5/2} + ln({\frac{T}{T_0}})^{3/2} + ln({\frac{V}{V_0}}))$

where s_0 is a constant, N the number of particles, T the temperature and V the volume.

and the incorrect is (derived assuming N is constant)

S=$Nk (ln({\frac{T}{T_0}})^{3/2} + ln({\frac{V}{V_0}}))$

my question is,

the incorrect expression allows for negative entropies which is not possible, is this the only reason property of entropy this equation doesn't satisfy?

the other thing is showing that this isnt a problem with the correct expression, the only way to show this is to say that s_0 must be larger then the negative terms (the negation will depend on the system, if N > N_0 then V > V_0, so the ln(V/V_0) will be +, then theres two possibilities for T/T_0.)

is that the only way to show that the correct expression is always positive?

are there any other properties the incorrect expression doesnt satisfy that the correct expression does satisfy?