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- define the chemical potential in terms of derivatives of the ĈE energy E and enthalpy H. For a one component system, these are u= ON and Evaluate these expressions for an ideal gas and compare to ON µ = -kT In (kT/PA³ ) from H=| P,s OF and |= 1 TP ON v.rQ2/ For the harmonic oscillator in classical limit, if the partition function is given by Z(B) = 1/(ßħw)N, find the entropy and internal energy. Q3/ Prove that F = -KTlnz .Calculate the number of microstates that are available in a single atom of carbon in graphite.The standard molar entropy (S°) of carbon is 5.7 J/(mol · K) and the Boltzmann constant (kB) is1.381 × 10 ―23?/?. HELP PLEASE
- The first excited energy level of a hydrogen atom has an energy of10.2 eV, if we take the ground-state energy to be zero. However, the first excited level is really four independent states, all with the same energy. We can therefore assign it an entropy of 8 = kIn 4, since for this given value of the energy, the multiplicity is 4. Question: For what temperatures is the Helmholtz free energy of a hydrogen atom in the first excited level positive, and for what temperatures is it negative?Problem 1. For the system of N spins (see the lecture notes), with energy e separating individual spin-down states from spin-up states, express the total internal energy U(T) of the system via its temperature T in equilibrium. Problem 2. For the same system of N spins, express its entropy S(T) via temperature T in equilibrium.Problem 1: In statistical mechanics, the internal energy of an ideal gas is given by: N. aNkB 2/3 (3NKB U = U(S,V) = е where a is a constant. 1- Show that the variation of the internal energy is given by: 2 dS - \3V 2 dU = dV \3NkB 2- Using the fundamental relation of thermodynamic dU = T.ds – p. dV, show that the equation of state PV = nRT follows from the first expression of U.
- A molecule has states with the following energies: 0, 1ε, 2ε, 3ε, and 4ε, where ε = 1.0 x 10-20 J. Calculate the probability that a molecule is in the ground state (with zero energy) for a collection of molecules in thermal equilibrium at T = 300 K. Provide your answer as a number in normal form to 3 decimal places (in the form X.XXX). It is a good idea to keep 4 decimal places during your calculation, then round to 3 decimal places for your submitted answer. Hint: note that this molecule has a finite number of states so you must take a finite sum, do not use expressions for infinite sums. Also note that your calculations for this problem will be useful for the next two problems, so keep them.Hi, could I get some help with this micro-macro connection physics problem involving root mean square speed? The set up is: What is the rms speed (in m/s) of a helium-3 atom in an ideal gas at a room temperature of 300 kelvin (K) to 4 digits of precision if kB = 1.38e-23 J/K, and the mass of helium-3 is 3.016 u, where the atomic mass unit u = 1.66e-27 kg? Thank you.A diatomic hydrogen gas H₂ is composed of two atoms of hydrogen connected by a spring of spring stiffness k. The probability to find the atoms at a position x is given by: f(x) = {Aexp[-Bx] for 0≤x≤ ∞ elsewhere where A is the normalization constant and ẞ a constant characteristic of the gas. 1. Draw a graph of the probability function. 2. Find an expression of A in terms of B. 3. Using the average elastic potential of the spring connecting the two atoms find an expression of in terms of k. 4. Assuming that the centre of mass of the two atoms moves with a constant speed v = and using the total average translational kinetic energy of the centre of mass find an expression of k in terms of the mass of the hydrogen atom m and the time t. [Note that the centre of mass, M = m/2.] 5. Assuming that the atoms rotated around an axis which is the perpendicular bisector of the line joining the two atoms and using the average rotational energy of the atoms, taking v = rw, r is the separation…
- The potential energy of two atoms in a diatomic molecule is approximated by U(r) = a/r12-b/r6, where r is the spacing between atoms and a and b are positive constants. Suppose the distance between the two atoms is equal to the equilibrium distance found in part A. What minimum energy must be added to the molecule to dissociate it - that is, to separate the two atoms to an infinite distance apart? This is called the dissociation energy of the molecule. Express your answer in terms of the variables a and b. For the molecule CO, the equilibrium distance between the carbon and oxygen atoms is 1.13\times 10-10m and the dissociation energy is 1.54\times 10-18J per molecule. Find the value of the constant a. Express your answer in joules times meter in the twelth power. Find the value of the constant b. Express your answer in joules times meter in the sixth power.Consider two blocks of copper. Block A contains 800 atoms and initially has a total of 20 quanta of energy. Block B contains 200 atoms and initially has 80 quanta of energy. The two blocks are placed in contact with each other, inside an insulated container (so no thermal energy can be exchanged with the surroundings).After waiting for a long time (for example, an hour), which of the following would you expect to be true? A. The entropy of block A is equal to the entropy of block B. B. Approximately 50 quanta of energy are in block A, and approximately 50 quanta of energy are in block B. C. Approximately 80 quanta of energy are in block A, and approximately 20 quanta of energy are in block B. D. The temperature of block A and the temperature of block B are equal.as a child, we were taught about molecules and atoms and how they work. now we are grown up and taught more in detail this time. let's say we have a ΑΒ U (r)=- 12 r r diatOmic molecule with (potential energy) A~> THIS IS A + CONSTANT ~> THIS IS A + CONSTANT r~> separation between da at0ms :( В dis potential is due to our force dat will compact all da atoms togetha FIND: a) pls get the equil1brium seperation (da distance betwe3n da atomz) b) pls also tell me if da force between them atoms are good or no if r is bigger than what (a) is. c) pls also tell me if da force between them atoms are good(attraction) or no (revulsion) if r is smaller than what (a) is. thank you so much. please help. i really need it