Carbon monoxide poisoning
- Equilibrium Absorbtion
- face Chemical potential and Gibbs distribution
face Lecture
120 min.
Chemical potential and Gibbs distribution
Thermal and Statistical Physics 2020chemical potential Gibbs distribution grand canonical ensemble statistical mechanics
These notes from the fifth week of Thermal and Statistical Physics cover the grand canonical ensemble. They include several small group activities. - computer Blackbody PhET
computer Computer Simulation
30 min.
Blackbody PhET
Contemporary Challenges 2022 (4 years) Students use a PhET to explore properties of the Planck distribution. - face Wavelength of peak intensity
face Lecture
5 min.
Wavelength of peak intensity
Contemporary Challenges 2022 (3 years) This very short lecture introduces Wein's displacement law. - assignment Diatomic hydrogen
assignment Homework
Diatomic hydrogen
rigid rotor hamiltonian angular momentum ground state hydrogen diatomic probability Energy and Entropy 2021 (2 years)At low temperatures, a diatomic molecule can be well described as a rigid rotor. The Hamiltonian of such a system is simply proportional to the square of the angular momentum \begin{align} H &= \frac{1}{2I}L^2 \end{align} and the energy eigenvalues are \begin{align} E_{\ell m} &= \hbar^2 \frac{\ell(\ell+1)}{2I} \end{align}
What is the energy of the ground state and the first and second excited states of the \(H_2\) molecule? i.e. the lowest three distinct energy eigenvalues.
At room temperature, what is the relative probability of finding a hydrogen molecule in the \(\ell=0\) state versus finding it in any one of the \(\ell=1\) states?
i.e. what is \(P_{\ell=0,m=0}/\left(P_{\ell=1,m=-1} + P_{\ell=1,m=0} + P_{\ell=1,m=1}\right)\)At what temperature is the value of this ratio 1?
- At room temperature, what is the probability of
finding a hydrogen molecule in any one of the \(\ell=2\) states versus
that of finding it in the ground state?
i.e. what is \(P_{\ell=0,m=0}/\left(P_{\ell=2,m=-2} + P_{\ell=2,m=-1} + \cdots + P_{\ell=2,m=2}\right)\)
- assignment Undo Formulas for Reduced Mass (Algebra)
assignment Homework
Undo Formulas for Reduced Mass (Algebra)
Central Forces 2023 (2 years) For systems of particles, we used the formulas \begin{align} \vec{R}_{cm}&=\frac{1}{M}\left(m_1\vec{r}_1+m_2\vec{r}_2\right) \nonumber\\ \vec{r}&=\vec{r}_2-\vec{r}_1 \label{cm} \end{align} to switch from a rectangular coordinate system that is unrelated to the system to coordinates adapted to the center-of-mass. After you have solved the equations of motion in the center-of-mass coordinates, you may want to transform back to the original coordinate system. Find the inverse transformation, i.e. solve for: \begin{align} \vec{r}_1&=\\ \vec{r}_2&= \end{align} Hint: The system of equations (\ref{cm}) is linear, i.e. each variable is to the first power, even though the variables are vectors. In this case, you can use all of the methods you learned for solving systems of equations while keeping the variables vector valued, i.e. you can safely ignore the fact that the \(\vec{r}\)s are vectors while you are doing the algebra. - group Box Sliding Down Frictionless Wedge
group Small Group Activity
120 min.
Box Sliding Down Frictionless Wedge
Theoretical Mechanics (4 years) Students solve for the equations of motion of a box sliding down (frictionlessly) a wedge, which itself slides on a horizontal surface, in order to answer the question "how much time does it take for the box to slide a distance \(d\) down the wedge?". This activities highlights finding kinetic energies when the coordinate system is not orthonormal and checking special cases, functional behavior, and dimensions. - assignment Undo Formulas for Reduced Mass (Geometry)
assignment Homework
Undo Formulas for Reduced Mass (Geometry)
Central Forces 2023 (3 years)The figure below shows the position vector \(\vec r\) and the orbit of a “fictitious” reduced mass \(\mu\).
- Suppose \(m_1=m_2\), Sketch the position vectors and orbits for \(m_1\) and \(m_2\) corresponding to \(\vec{r}\). Describe a common physics example of central force motion for which \(m_1=m_2\).
- Repeat, for \(m_2>m_1\).
- group Optical depth of atmosphere
group Small Group Activity
30 min.
Optical depth of atmosphere
Contemporary Challenges 2022 (4 years) In this activity students estimate the optical depth of the atmosphere at the infrared wavelength where carbon dioxide has peak absorption. - group Flux through a Cone
group Small Group Activity
30 min.
Flux through a Cone
Static Fields 2021 (4 years) Students calculate the flux from the vector field \(\vec{F} = C\, z\, \hat{z}\) through a right cone of height \(H\) and radius \(R\) . - assignment Cone Surface
assignment Homework
Cone Surface
Static Fields 2023 (6 years)- Find \(dA\) on the surface of an (open) cone in both cylindrical and spherical coordinates. Hint: Be smart about how you coordinatize the cone.
- Using integration, find the surface area of an (open) cone with height \(H\) and radius \(R\). Do this problem in both cylindrical and spherical coordinates.
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Thermal and Statistical Physics 2020
In carbon monoxide poisoning the CO replaces the \(\textsf{O}_{2}\) adsorbed on hemoglobin (\(\text{Hb}\)) molecules in the blood. To show the effect, consider a model for which each adsorption site on a heme may be vacant or may be occupied either with energy \(\varepsilon_A\) by one molecule \(\textsf{O}_{2}\) or with energy \(\varepsilon_B\) by one molecule CO. Let \(N\) fixed heme sites be in equilibrium with \(\textsf{O}_{2}\) and CO in the gas phases at concentrations such that the activities are \(\lambda(\text{O}_2) = 1\times 10^{-5}\) and \(\lambda(\text{CO}) = 1\times 10^{-7}\), all at body temperature \(37^\circ\text{C}\). Neglect any spin multiplicity factors.
First consider the system in the absence of CO. Evaluate \(\varepsilon_A\) such that 90 percent of the \(\text{Hb}\) sites are occupied by \(\textsf{O}_{2}\). Express the answer in eV per \(\textsf{O}_{2}\).
Now admit the CO under the specified conditions. Fine \(\varepsilon_B\) such that only 10% of the Hb sites are occupied by \(\textsf{O}_{2}\).