ENERGY CONSERVATION IN SWEPT FIELD LIMIT For a calorimeter sample (plus addenda) weakly thermally linked to a temperature controlled reservoir, energy conservation implies -T dS = \kappa \Delta T dt + C_{} dT where κ is the sample to reservoir thermal conductance and addenda is the heat capacity of the actual addenda (such as the thermometer, heater, and glue or grease binding the sample to the sensors) plus the heat capacity of the sample lattice (due to phonons). The left hand side term is the heat released by the system — which in the case of a spin system, for example, would be the heat released by the spins — when the field is changed by dH. The minus sign indicates that system entropy decreases as heat is released. Most of the released heat flows to the reservoir but some fraction heats up the addenda (to the same temperature as the system). The first term on the right hand side describes heat flow to the reservoir. The second term describes the temperature rise of the addenda. In a non-adiabatic relaxation-time or ac-calorimeter like that used in our swept-field measurements , the first term dominates. In contrast, in an adiabatic measurement, the first term is negligible.

_Abstract_ In order to determine what spiral galaxies are composed of, we have to find their mass and their luminosity to produce a mass/luminosity ratio. This will help us determine what spiral galaxies are composed of because we can compare their mass/luminosity ratios to known stellar mass/luminosity ratios. By comparing these two different mass/luminosity ratios, we can determine if galaxies are composed mostly of stellar material. In this report, I will be analyzing 26 different spiral galaxies by finding their mass, their luminosity, and their mass/luminosity ratio. By using these techniques, I will show that only 10% of the total galactic mass is made of stellar material and that 90% of a galaxy is composed of non luminous “dark matter.”

AIMS The goal of the Franck-Hertz experiment is to demonstrate that electrons occupy only discrete, quantized energy states for neon and argon atoms.

Two sources of noise, Johnson noise and shot noise, are investigated in this experiment. The Johnson noise which is the voltage fluctuations across a resistor that arose from the random motion of electrons. It was measured across different resistances and at different bandwidths at room temperature, resulting in a calculation of the Boltzmann constant of 1.46 ⋅ 10−23 m² kg s−2 K−1 ± 2.5 ⋅ 10−21 m² kg s−2 K−1 and 1.46 ⋅ 10−23 m² kg s−2 K−1 ± 2.6 ⋅ 10−21 m² kg s−2 K−1. The shot noise occurs due to the quantization of charge, and was measured by varying current in the system, with which we calculated the electron charge of 1.64 ⋅ 10−19 ± 7.0 ⋅ 10−22. They agree quite well with the accepted values of 1.38064852 ⋅ 10−23 m² kg s−2 K−1, and 1.64 ⋅ 10−19C for the Boltzmann constant and electron charge respectively. Errors are discussed.

ABSTRACT The lowest excitation energy of the elements Neon, Mercury, and Argon was determined by analyzing the fundamental properties of the signal structure in the Franck-Hertz experiment. In order to accurately determine the lowest excitation energy a new method proposed in was employed. The main idea is that the spacings between the minima in the Franck Hertz curve increase linearly due to the additional acceleration over the mean free path. Therefore a linear fit was applied to graphs of spacings ΔE versus minimum order n. The fit estimated the lowest excitation energies of Neon (19.54 ± 1.48eV), Mercury (4.72 ± .25eV), and Argon (11.36 ± .38eV) accurately within experimental uncertainty.

ABSTRACT We performed an experiment to measure the Faraday rotation of polarized light passing through a magnetic field, as well as measuring the Verdet constant of an SF57 glass tube with a length of 0.1 m. Our results are consistent with the general idea of Faraday rotation, which suggests that linearly polarized light experiences rotation when applying a magnetic field. The values we found for the Verdet constant are $20.7 \pm 0.845 {T \cdot m}$, $21.095\pm 4.12 {T \cdot m}$ and $20.43 \pm 0.058 {T \cdot m}$, and those values are consistent with each other within uncertainty.

SIGNIFICANCE OF THE EXPERIMENT In their 1914 experiment, James Franck and Gustav Hertz demonstrated that in collisions between accelerated electrons and gaseous atoms, energy was only transferred from the electrons to the atoms if the electron had gained an energy before the collision equal to or greater than the energy required to excite the atom from its ground state to its next lowest energy level. If it had more energy than needed, the electron only transferred the amount corresponding to the energy difference between the two atomic energy levels. That is, atoms have discrete, quantized energy states, providing early evidence for the validity of quantum theory. Franck and Hertz won the 1925 Nobel Prize in recognition of this result.

NUCLEAR SCHOTTKY EFFECT In the presence of a magnetic field, the energy levels of a nucleus with spin I split into 2I + 1 levels. This effect — known as the nuclear Zeeman effect — leads to hyperfine splitting of energy levels when the nuclei are in a local magnetic field and a field and temperature dependent contribution to the specific heat. In closed form , c_N = R \left({2I}\right)^2 \left[{}^2\left({2I}\right) - (2I+1)^2 {}^2\left[(2I+1)\left({2I}\right)\right]\right] where x = _N I H}{k_B T} The Zeeman splitting of the nuclear energy levels leads to a broad peak in the specific heat when kbT is on the order of the energy splitting μH, but because the energy splittings are small[1], only the high temperature (μH/kBT)² tail of specific heat peak is usually seen. In that limit, and assuming that the zero field field splitting (ZFS) is negligible in comparison to that from the applied field H, then , c_N(T,H) = _N}{\mu_0}\left({T}\right)^2 where μ₀ = 4π ⋅ 10−7 H/m and the nuclear Curie constant λN is given by {\mu_0} = N_A I (I+1)_N g_N\right)^2}{3 k_B} \left[}{^2}}\right]}. where here gN = μ/I and μN is the nuclear magneton $\mu_N = {4 \pi M_p c} = 5.051 10^{-27} $. It is often convenient to express this Zeeman splitting of the nuclear energy levels in temperature units. In this case \Delta = g \mu_n H / k_B . [1] the nuclear magneton is a factor of 1836.1 smaller than the Bohr magneton μB

AIMS The Faraday Rotation of Polarized light is the rotation of the plane of polarization of light propagating through a medium due to the presence of a magnetic field. In this experiment, we aim to measure the Verdet constant of a glass rod (SF-57) through the Faraday Effect.

ABSTRACT We performed an experiment to measure the Faraday rotation of polarized light passing through a magnetic field, as well as measuring the Verdet constant of a glass tube with a length of 0.1 m. Linearly polarized light from a HeNe laser was sent through a magnetic field created by a solenoid. The light then passed through an adjustable polarizer and was detected by a photodiode. Using the photodiode, we measured how the intensity of the light changed when turning the polarizer through 360 degrees. We performed this experiment both with and without a glass tube inside the solenoid. We plotted the data as a function of voltage versus angle in plotly in order to find the angle where the voltage measured by the photodiode changed most rapidly. By keeping the polarizer at its most sensitive angle, we plotted voltage versus magnetic field and measured how the voltage changed with magnetic field. We used the lock-in amplifier to make the voltage measurement more accurate.

ABSTRACT As written, my draft abstract is too long, but it focuses on the key points of this article (and significantly narrows the scope of the article). Some of the material should move into the main body of the article. We present an improved method for temperature control of an ICE-Oxford Variable Temperature Insert (VTI) at temperatures below 4.2 K (down to a base temperature of 1.3 K for our system). The closed cycle VTI is part of a liquid-cryogen-free ICE-OXford cryostat; the sample probe is thermally linked to the VTI through the use of a small amount of He exchange gas, allowing the temperature of the sample probe to be raised above that of the VTI. In both the original (ICE-Oxford) and our improved design, the temperature of the VTI is controlled by measuring and controlling the vapor pressure of the VTI 4He bath. A sealed pump continually pumps on the VTI helium space; the liquid helium fill rate for the VTI is adjusted through analog control of an motor-controlled needle valve. A 10 V input to the servo motor controller causes the needle valve to fully open, while a 0 V input causes the needle value to fully close. Using the as supplied method, we were able to control the pressure with a precision of ±0.2 mbar but with an absolute accuracy of only 2 mbar. With better choice of PID settings, it might be possible to reduce the systematic offset in the pressure stepping, but not overall precision. This is because the as supplied method uses a computer to directly read the low-resolution (±0.1 mbar) digital output of the pressure gauge. The speed with which the software-based PID controller can update the output of the computer D to A board (or, originally, on of the additional analog outputs of a Lake Shore temperature controller) is further limited by the update rate of the digital display. Our improved method of temperature control improves the precision and absolute accuracy of the pressure control by an order of magnitude: ±0.02 mbar or better in precision and ±0.2 mbar in absolute accuracy (compared to the setpoint). To do this, we make two changes the nature of the PID control of the needle valve servo-motor and the manner in which the He vapor pressure is read by the PID controller. First, instead of using a computer to read the and then a low speed software PID control loop to produce the analog voltage input needed by the motor controller, we indirectly measure the higher resolution (±0.005 mbar) analog voltage output of the pressure gauge and, in addition, use an analog PID controller to hold that voltage at the desired setpoint.