PS4Solutions

PS4Solutions - Chemistry 120B SP11 Problem Set 4 Solutions...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chemistry 120B SP11 Problem Set 4 Solutions Total: 50 points 1. (5 points) See MQS Solutions Manual. 2. (i) (4 points) The number of possible locations for a single particle is V/λ 3 , where λ is the thermal deBroglie wavelength, λ = h/ √ 2 πmk B T . q = V λ 3 Because the particles are statistically independent, the total partition function factorizes. Q = q N N ! = 1 N ! V λ 3 N ∝ V N Taking the log of the partition function, ln Q = N ln V + (stuff independent of V) Differentiating with respect to volume at constant temperature and number of molecules, ∂ ln Q ∂V β,N = βp = N V pV = Nk b T Or, pV = nRT where n is the number of moles. (ii) (3 points) Q ∝ ( V- Nb ) N lnQ = N ln( V- Nb ) + (stuff independent of V) ∂ ln Q ∂V β,N = βp = N V- Nb p ( V- Nb ) = Nk B T (iii) (3 points) Unlike particles in an ideal gas, the particles in this system take up space and interact with each other. For an interaction volume only slightly larger than a particle, a tagged particle sitting at the sphere’s center will restrict the number of other particles that can fit inside the sphere. Also, becausesphere’s center will restrict the number of other particles that can fit inside the sphere....
View Full Document

{[ snackBarMessage ]}

Page1 / 4

PS4Solutions - Chemistry 120B SP11 Problem Set 4 Solutions...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online