Statistical weight (thermodynamics)

[quietrain]

Homework Statement

find the equation of state which gives the relationship between P , V , N and T

C and b are constants

Ω = Ce^bNV2(EV)^N

Homework Equations

P/T = (ds/dV)_E,N

The Attempt at a Solution

so i just use s = klnΩ ?

then i get ds/dV = k2bNV

so P = k2bNVT ? that's it?

btw, what does the E and N in (ds/dV)_E,N tells me? is it mean keep E and N constant? or the differential is specified by the terms E and N?

thanks!

 

[G01]

Homework Statement

find the equation of state which gives the relationship between P , V , N and T

C and b are constants

Ω = Ce^bNV2(EV)^N

Homework Equations

P/T = (ds/dV)_E,N

The Attempt at a Solution

so i just use s = klnΩ ?

then i get ds/dV = k2bNV

so P = k2bNVT ? that's it?

That seems like the correct method, but double check your derivative. You have a factor of V inside the logarithm, so you should have a second term in your derivative corresponding to differentiating the log(EV) and not V^2

btw, what does the E and N in (ds/dV)_E,N tells me? is it mean keep E and N constant?

Yes, that is what it means.

 

[quietrain]

ah i see thank you!