Spin Fermi Estimate

• assignment Heat of vaporization of ice

  assignment Homework

  Heat of vaporization of ice

  Vaporization Heat Thermal and Statistical Physics 2020 The pressure of water vapor over ice is 518 Pa at \(-2^\circ\text{C}\). The vapor pressure of water at its triple point is 611 Pa, at 0.01\(^\circ\text{C}\) (see Estimate in \(\text{J mol}^{-1}\) the heat of vaporization of ice just under freezing. How does this compare with the heat of vaporization of water?
• assignment Derivatives from Data (NIST)

  assignment Homework

  Derivatives from Data (NIST)

  Energy and Entropy 2021 (2 years) Use the NIST web site “Thermophysical Properties of Fluid Systems” to answer the following questions. This site is an excellent resource for finding experimentally measured properties of fluids.

  1. Find the partial derivatives \[\left(\frac{\partial {S}}{\partial {T}}\right)_{p}\] \[\left(\frac{\partial {S}}{\partial {T}}\right)_{V}\] where \(p\) is the pressure, \(V\) is the volume, \(S\) is the entropy, and \(T\) is the temperature. Please find these derivatives for one gram of methanol at one atmosphere of pressure and at room temperature.
  2. Why does it take only two variables to define the state?
  3. Why are the derivatives above different?
  4. What do the words isobaric, isothermal, and isochoric mean?
• group de Broglie wavelength after freefall

  group Small Group Activity

  30 min.

  de Broglie wavelength after freefall

  Contemporary Challenges 2021 (4 years)

  de Broglie wavelength gravity

  In this activity students combine energy conservation with the relationship between the de Broglie wavelength and momentum to find the wavelength of atoms that have been dropped a given distance.
• assignment Calculation of $\frac{dT}{dp}$ for water

  assignment Homework

  Calculation of \(\frac{dT}{dp}\) for water

  Clausius-Clapeyron Thermal and Statistical Physics 2020 Calculate based on the Clausius-Clapeyron equation the value of \(\frac{dT}{dp}\) near \(p=1\text{atm}\) for the liquid-vapor equilibrium of water. The heat of vaporization at \(100^\circ\text{C}\) is \(2260\text{ J g}^{-1}\). Express the result in kelvin/atm.
• group Going from Spin States to Wavefunctions

  group Small Group Activity

  60 min.

  Going from Spin States to Wavefunctions

  Quantum Fundamentals 2023 (2 years)

  Wavefunctions quantum states probability amplitude histograms matrix notation of quantum states Arms representation

  Arms Sequence for Complex Numbers and Quantum States

  Completeness Relations

  Students review using the Arms representation to represent states for discrete quantum systems and connecting the Arms representation to histogram and matrix representation. The student then extend the Arms representation to begin exploring the continuous position basis.
• group Ideal Gas Model

  group Small Group Activity

  30 min.

  Ideal Gas Model

  Ideal Gas surfaces thermo

  Students consider whether the thermo surfaces reflect the properties of an ideal gas.
• assignment Wavefunctions

  assignment Homework

  Wavefunctions

  Quantum Fundamentals 2023 (3 years)

  Consider the following wave functions (over all space - not the infinite square well!):

  \(\psi_a(x) = A e^{-x^2/3}\)

  \(\psi_b(x) = B \frac{1}{x^2+2} \)

  \(\psi_c(x) = C \;\mbox{sech}\left(\frac{x}{5}\right)\) (“sech” is the hyperbolic secant function.)

  In each case:

  1. normalize the wave function,
  2. plot the wave function using Mathematica or other computer plotting tool (be sure to include the code you used and label your plots/axes appropriately),
  3. find the probability that the particle is measured to be in the range \(0<x<1\).

• face Statistical Analysis of Stern-Gerlach Experiments

  face Lecture

  30 min.

  Statistical Analysis of Stern-Gerlach Experiments

• face Compare \& Contrast Kets \& Wavefunctions

  face Lecture

  30 min.

  Compare & Contrast Kets & Wavefunctions

  Bra-Ket Notations Wavefunction Notation Completeness Relations Probability Probability Density

  Completeness Relations

  In this lecture, the instructor guides a discussion about translating between bra-ket notation and wavefunction notation for quantum systems.
• assignment Find Area/Volume from $d\vec{r}$

  assignment Homework

  Find Area/Volume from \(d\vec{r}\)

  Static Fields 2023 (5 years)

  Start with \(d\vec{r}\) in rectangular, cylindrical, and spherical coordinates. Use these expressions to write the scalar area elements \(dA\) (for different coordinate equals constant surfaces) and the volume element \(d\tau\). It might help you to think of the following surfaces: The various sides of a rectangular box, a finite cylinder with a top and a bottom, a half cylinder, and a hemisphere with both a curved and a flat side, and a cone.

  1. Rectangular: \begin{align} dA&=\\ d\tau&= \end{align}
  2. Cylindrical: \begin{align} dA&=\\ d\tau&= \end{align}
  3. Spherical: \begin{align} dA&=\\ d\tau&= \end{align}

• Quantum Fundamentals 2023 (2 years) The following two problems ask you to make Fermi estimates. In a good Fermi estimate, you start from basic scientific facts you already know or quantities that you can reasonably estimate based on your life experiences and then reason your way to estimate a quantity that you would not be able guess. You may look up useful conversion factors or constants. Use words, pictures, and equations to explain your reasoning:
  1. Imagine that you send a pea-sized bead of silver through a Stern-Gerlach device oriented to measure the z-component of intrinsic spin. Estimate the total z-component of the intrinsic spin of the ball you would measure in the HIGHLY improbable case that every atom is spin up.
  2. Protons, neutrons, and electrons are all spin-1/2 particles. Give a (very crude) order of magnitude estimate of the number of these particles in your body.