Partition Function Homework: Find Entropy Change for Isothermal Expansion

  • Thread starter Thread starter senan
  • Start date Start date
  • Tags Tags
    Function
senan
Messages
17
Reaction score
0

Homework Statement



One mole of a gas obeys the equation of state
(P +a/V2 )(1 −b/V) =RT/V
Find the change in entropy if one mole of the gas is isothermally expanded until the volume
is doubled. Express your answer in terms of the initial volume of the gas Vi.

Homework Equations



S2-S1=1/T Integral from Vi to 2Vi of PdV

The Attempt at a Solution



I replaced P with P=NkT/V

that leads to

S2-S1=-kln(2Vi/Vi)

as the answer was asked for in terms of Vi I'm not sure that's rightsorry titled the question wrong meant to title other Q as partition function
 
Last edited:
Physics news on Phys.org
That is not right.

You are using the wrong equation of state.

It is stated in problem that the gas obeys a different equation of state, not the usual, PV=NkT.

You have to use the given equation of state to express P in terms of V.
 
By the way, that equation of state is called the van der Waals equation. It takes into account intermolecular forces and the volume of molecules instead of assuming an ideal gas.
 

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Number of quantum accessible states of a particle given T, N?'

It's given a gas of particles all identical which has T fixed and spin S. Let's ##g(\epsilon)## the density of orbital states and ##g(\epsilon) = g_0## for ##\forall \epsilon \in [\epsilon_0, \epsilon_1]##, zero otherwise. How to compute the number of accessible quantum states of one particle? This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system. Simply, if we have the density of orbitals we have to integrate ##g(\epsilon)## and we have...
View full post »

Similar threads

Change in entropy, quasistatic, isothermal expansion
Replies
6
Views
3K
Is the Entropy in a Free Expansion Affected by the Gas Type?
Replies
8
Views
2K
Partition function, Ideal gas, Entropy
Replies
2
Views
3K
Change in Entropy for Isothermal Expansion
Replies
3
Views
8K
Stat-Mech problem: pressure from a partition function
Replies
4
Views
2K
How Is Work Calculated in an Isothermal Expansion of an Ideal Gas?
Replies
2
Views
2K
Partition Function at a Fixed Pressure
Replies
1
Views
2K
Finding compressibility from given internal Energy function
Replies
7
Views
2K
Reversible adiabatic expansion -- calculate change in E
Replies
8
Views
2K
How is Entropy Change Calculated for a Composite System?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top