PS6Sol_f10 - Physics 112 Fall 2010 Professor William...

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 DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 112 Fall 2010 Professor William Holzapfel Homework 6 Solutions Problem 1, Kittel 5.1: Centrifuge When the gas is in equilibrium, we know that the total chemical potential will be constant through- out. The total chemical potential is = int + ext , and we know that the internal chemical potential (of an ideal gas) is related to the number density by = ln n ( r ) n Q , so we see that a spatial variation in the external chemical potential will create a spatially varying number density. A rotating gas feels a centrifugal force F = Mv 2 /r = Mr 2 . We can consider this force to be caused by an effective potential such that F =- dV/dr : ext ( r ) = V ( r ) =- Z drF ( r ) =- M 2 r 2 2 . The total chemical potential ( r ) = ln n ( r ) n Q- M 2 r 2 2 will be constant throughout the centrifuge in equilibrium, so we can equate the chemical potential at a radius r with the chemical potential at the axis of rotation: (0) = ln n (0) n Q = ln n ( r ) n Q- M 2 r 2 2 = ( r ) Solving for n ( r ) we have: n ( r ) = n (0) exp Mr 2 2 2 (1) So we see that we get an exponentially higher concentration of particles at larger r (as expected). Problem 2, Kittel 5.4: Active Transport We know that the ratio of the concentration of K + is n sap /n water = 10 4 , so we can find the difference in the chemical potentials of K + of the sap and the water by treating the ions as an ideal gas: 4 = sap- water = ln n sap n Q- ln n water n Q = ln n sap n water = ln(10 4 ) = (300 K ) k b * 4 ln(10) = (1200 K) ( 1 . 38...
View Full Document

Page1 / 4

PS6Sol_f10 - Physics 112 Fall 2010 Professor William...

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