exam1 - YOUR NAME HERE March 4, 2009 Chem 120B Midterm #1...

Info iconThis preview shows pages 1–3. 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: YOUR NAME HERE March 4, 2009 Chem 120B Midterm #1 Definitions and Useful Formulas: Inverse temperature: = 1 k B T Boltzmann distribution: P ( ) = e- E Q Partition function: Q = summationdisplay e- E Equilibrium averages: ( E ) = parenleftbigg ln Q parenrightbigg N,V , ( E 2 ) = parenleftbigg 2 ln Q 2 parenrightbigg N,V = k B T 2 C V Equipartition principle: ( E ) = 1 2 k B T per clasical degree of freedom with quadratic energy. Entropy: S = k B ln W, S = k B summationdisplay P ( ) ln P ( ) First and second laws of thermodynamics: dE = dw + dq, dS dq T Gaussian integration: integraldisplay - dx e- x 2 / (2 2 ) = 2 2 , 1 2 2 integraldisplay - dx x 2 e- x 2 / (2 2 ) = 2 Questions on this exam concern a long chain molecule, composed of N + 1 particles linked by N bonds, which can exchange energy with a heat bath at temperature T . Quantum mechanical effects can be ignored throughout. 1 1. Consider first a model in which consecutive particles in the chain are connected by springs and can move continuously in three-dimensional space, as sketched below. . . . r 1 r 2 r 3 r 4 ... r N-1 r N (The light gray curve represents the segment of this molecule whose particles and bonds are not explicitly shown.) The bond vector r j pointing from particle # j to particle # j + 1 has components x j , y j , and z j along x-, y-, and z-axes of the laboratory frame. The length of the j th bond is therefore | r j | = radicalBig x 2 j + y 2 j + z 2 j . This potential energy of this model chain molecule has independent contributions from each bond: U = N summationdisplay j =1 1 2 a | r j | 2 , where the bond stiffness a is a positive constant. The total energy is therefore E = K + U, where K is the kinetic energy for N + 1 particles of mass...
View Full Document

Page1 / 10

exam1 - YOUR NAME HERE March 4, 2009 Chem 120B Midterm #1...

This preview shows document pages 1 - 3. Sign up to view the full document.

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