Tin can exist in two forms, grey tin (also called alpha, a brittle and non-conductive form) and white tin (also called beta, the metallic form that conducts electricity). Gray tin is the stable form at low temperatures and white tin the stable form at high temperatures. There is a phase transition between the two phases with a transition temperature of 286 K at a pressure of 1.00 atm. What is the change in this transition temperature if the pressure is increased to 100 atm? (The latent heat for the transition is 2.20 × 10³J/mol. The density of grey and white tin are 5.77 × 103 kg/m³and 7.37 × 103 kg/m³. The atomic weight of tin is 118.7.)
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- a) Calculate the characteristic temperature associated with a vibrational energy level transition of angular frequency ω = 2×1013 rad s-1 . b). A process “freezes out” at temperatures below 42 K. Calculate the typical energy associated with this process.1. A model for the potential energy interaction between the two nitrogen atoms in the N2 molecule is proposed that has the form: v(4) = 4E, (4)* - ()'] 12 a. Find the position of the potential minimum and its value there, in terms of o and Eo, respectively. What do these parameters represent physically about the molecule? b. Draw a hand sketch of V(r) showing rmin, V(rmin) and where V crosses the r axis. c. If the atom is disturbed from its equilibrium by a small amount, show that the 7.56. frequency of oscillation is w = d. For molecular nitrogen, the bond length is 1.1 x 10-1°m, the bond (binding) energy is 9.79 eV (15.66 x 10-19 J), the mass is 14 amu = 23.38 x 10-27 kg. In the spectroscopy laboratory, this vibration is measured to be 8.8 x 1013 Hz. Is this a good model for the interatomic potential? (Recall o = 2n times frequency in Hz) where m is the mass of a nitrogen atom.Consider 1.5 mol of pure nitrogen gas N2 which we will treat as a diatomic ideal gas. From 100 K to 1000 K, the gas has three translational and two rotational degrees of freedom. Above 1000 K, there are two additional vibrational degrees of freedom. The molar mass of N2 is 0.028 kg/mol. a. If the nitrogen molecules have an rms translational molecular speed of 511 m/s, what is the temperature of the gas? b. What is the internal energy U of the nitrogen gas at the temperature from part a? c. If the nitrogen gas has a pressure of 1.2 atm, what volume (in liters) does it occupy at the temperature from part a? d How much heat would be required to raise the temperature of the gas from 1500 K to 1800 K, at a constant volume? Remember that vibrational degrees of freedom are active at these temperatures.
- Nitrogen molecules are made of two nitrogen atoms with atomic weight of 14 each. Water molecules are made of one oxygen of 16 atomic mass units and two hydrogens of 1 atomic mass unit each. If you have one gram of each substance in vapor form, at high enough temperature that all molecular vibration and rotation modes are accessible, and the two substances are at the same temperature, what is the ratio of the total energy content of the nitrogen to that of the water?3 A one cm sample of a hypothetical material with conductivity of 108 (Ohm-meter) 1 is formed into a 10 cm wire. The material contains 1042 atoms per cm. Calculate the electron drift velocity when the wire carries an electrical potential of 10 V.Question B2 At low temperatures, a certain element has a hexagonal crystal structure with unit cell parameters a = 3.59 Å, c = 26.38 Å. The motif contains nine atoms at the fractional positions given in the following table: X y z 0 0 0 ○ 713 23 0 9 9 4959 23 79 13 23 13 23 0 23 ○ 23 0 23 13 23 -3 0 3 9 a) Calculate the angle 20 at which the first (lowest-angle) diffraction peak from this material will be observed using Cr Ka radiation of wavelength λ = 2.2896 Å. b) Crystallites (individual crystals) of this material have the form of flakes that are about 2 mm wide in the ab plane and about 2 μm thick in the c direction. Using a convolution argument, explain qualitatively what shape the diffraction peaks will have in 3D reciprocal space. c) Explaining your logic carefully, show that this is a close-packed structure. Give the layer sequence in ABC notation.
- Problem 2: Helium is a very important element for both industrial and research applications. In its gas form it can be used for welding, and since it has a very low melting point (only 0.95 K under 2.5 MPa) it can be used in liquid form to cool superconducting magnets, such as those found in particle physics experiments. Say we have a cylinder of n = 145 moles of Helium gas at room temperature (T = 20° C). The cylinder has a radius of r = 17.5 cm and a height h = 1.45 m. Part (a) What pressure (in kPa) is the helium gas under? P = ______ Part (b) Helium is usually kept in the highest pressure gas cylinders, which can typically withstand at least 500 atm of pressure. Would the tank in part (a) be able to maintain its structural integrity? Part (c) In principle, these tanks could fail if the temperature of the Helium started rising - if they were stored in a hot environment, for instance. To determine how much of a danger this is, calculate the temperature (in C) the Helium gas…A 5 L tank contains Argon gas at 55°C and 4.5 atm. Find the total translational kinetic energy of all the Argon atoms in the tank. 1 atm = 1.013 x 10^5 Pa 1 L = 10^-3 m^3 R= 8.314 J/K-mol Molar mass of Argon= 40 Kb=1.38 x 10 ^-23 J/KThe atomic radius of gold (Au) is 0.146 nm and its atomic mass is 197 gmol-1. Assuming the atoms to be hard spheres that touch each other along the face diagonals of the unit cell, calculate the density of its unit cell. Given Avogadro's number, NA = 6.023 X 1023 atoms mol-1.
- Plz correct solution part d and e.Q7. A copper rod, an aluminium rod and a brass rod, each of 6 m length and 1 cm diameter, are placed end to end, with the aluminium rod between the other two. The free end of the copper rod is placed in boiling water and the free end of the brass rod is placed in ice water. What is the steady-state temperature of the copper-aluminium junction? And the aluminium-brass junction?A cylinder of nitrogen and a cylinder of neon are at the same temperature and pressure. The mean free path of a nitrogen molecule is 160 nm. What is the mean free path of a neon atom? Express your answer with the appropriate units. ANe= Submit HÅ Value Units Previous Answers Request Answer ?