Answered: Obtain the expression for the average…

Obtain the expression for the average thermal energy when the partition function is Z: ħo (A) 극청고 2 (B) kzT 1 (C) -k,T 4 (D) 4k,T

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter2: The Kinetic Theory Of Gases

Section: Chapter Questions

Problem 68P: Using the method of the preceding problem, estimate the fraction of nitric oxide (NO) molecules at a...

See similar textbooks

Related questions

Q: Why is the entropy higher for a system with 5 particles with energy states >1 than for a system with…

A: Entropy increases precisely for energy states>1 because energy is conserved. To hold a…

Q: From the differentials of thermodynamic potentials: av dF = -SdT – PdV dG = -SdT + VdP dH = TdS +…

Q: Obtain relations for the characteristic lengths of a large plane wall of thickness 2L, a very long…

Q: *10 Show that the probability P(E) that an energy level having energy E is not occupied is P(E) =…

Q: The following data show the probabilities for the number of cars sold in a given day at Alex's ca…

Q: Consider 1.50 mols of a substance in thermal equilibrium at a temperature of 87.0 °C whose atoms can…

A: Consider 1.50 mols of a substance in thermal equilibrium at a temperature of 87.0 °C whose atoms can…

Q: Calculate the leading term in the temperature dependence of the bulk mod- ulus of the…

A: To calculate the leading term, => Bulk's modulus (B)

Q: Show that the most probable speed of the Maxwell-Boltzmann distribution of molecular speeds is given…

A: To show that, the most probable speed of the Maxwell-Boltzmann distribution of molecular speed is…

Q: For a system of fermions at room temperature, compute the probability of a single-particle state…

A: Given Data: The temperature is, T = 293 K. The expression for calculating the probability of a…

Q: Given that the internal energy U of blackbody radiation in a cavity of volume V at temperature T is…

A: Radiation pressure is defined as one third of the energy density per unit volume. Radiation pressure…

Q: Plot the Fermi function Vs. Energy at the temperature of 500 K, when EF = 2 eV

Q: 1)A missile protection system consists of n radar sets operating independently, each with…

Q: Q(3): Match between the followings definitions ( 1 In a steady-state Diffusion A Atom interchanges…

A: In the given question, We are asked to match the definition of Steady-state diffusion, Diffusion,…

Q: What is the probability that the electron tunnels through the barrier? (Use 9.11 10-31 kg for the…

A: Given data: The kinetic energy is: E = 3.10 eV The width of barrier is: L = 0.230 nm The mass of an…

Q: For a certain metal the stiffness of the interatomic bond and the mass of one atom are such that the…

A: Consider the number of atoms be n, the number of oscillators be N, the energy of one quanta be qE,…

Q: Show that z = N/Q. where Q = Is called the partition function.

A: Show the expression for the occupation number (nλ) as follows: The above expression represents the…

Q: an experiment, the temperature of a hot gas stream is to be measured by a thermocouple with a…

Q: Show that V (x) = 2 ln(tanh(x/2)) satisfies the Poisson– Boltzmann equation V"(x) = sinh(V (x)),…

A: Given, Vx =2×lntan hx2

Q: Define a random variable X : [0, 1] → R on the probability triple ([0, 1], B[0, 1],Leb ) by X(w) = –…

Q: Define the Partition Function using Boltzmann factors ?

A: Introduction: Statistical mechanics is the branch of physics where, the study of atoms, molecules,…

Q: Let f(ɛ) be the Fermi-Dirac distribution function and µ be the chemical potential. Obtain the…

Q: Consider the semiclassical model of N particles with two energy levels (0 and e > 0). Suppose that…

Q: Suppose you have an ideal gas of fermions at room temperature (293 K). How large must E EF be for…

Q: In an experiment, the temperature of a hot gas stream is to be measured by a thermocouple with a…

A: Write the expression for the lumped system approximation relation, and solve for the characteristic…

Q: The atoms in a solid possess a certain minimum zero-point energy even at 0 K, while no such…

A: According to the uncertainty principle, it is impossible to measure simultaneously both the position…

Q: From the clausius inequality, considering a closed system, fixed n, and PV work, show that the…

A: To proof that: (δGδn)T,P=μ

Q: tropy H(X | Y ) in terms of the joint distribution and associated conditional probabilit

A: Let us consider p(x, y) to be the joint probability distribution of the two random variables X and Y…

Q: Q 3: - A classic assembly consists of three energy segments with E = 0, 91 = 1 €2 0.0125 eV, 92 2 E3…

Q: A van der Waals dispersion force between helium atoms produces a very shallow potential well, with a…

A: The depth of potential is given as 1 meV. The energy needed to condense Helium be defined as,…

Q: WINDY 3 A wind measuring device took the following wind readings (in m/s) - | 5.1 | 3.2 | 2.8 | 5.3…

Q: For an ideal gas O2 at T = 293 K fi nd the two speeds v that satisfy the equation 2F(v) = F(v*).…

A: Given: An ideal gas of oxygen O2 Temperature: 293 [K] Maxwell`s distribution function: F(v) Mass of…

Q: Suppose that an energy level (j) includes 6 states (gj =6) and 3 particles (Nj =3). What will be the…

Q: A triatomic molecule can have a linear configuration, as does CO2 (as shown), or it can be…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts (a, b,…

Q: 4c sin M ka The dispersion relation of phonons in a monatomic, linear chain of atoms is given by:…

A: The maximum phonon frequency at the edge of the Brillouin zone is, wmax = √(4C/M) , where M is the…

Q: A particle is confined to the region 0<x<a on the x-axis and has a probability density P(x)…

A: We have probability density for a particle P(x)=1-cos(2*pi*x) in the region 0<x<a. We need to…

Q: Show that heat is a path function.

A: Consider a system taken from state 1 to 2 through the path P and it is returned to the original…

Q: Calculate the ratio of the number of vacancies in equilibrium at 27 C in aluminum to that produced…

A: No crystal is fully occupied by the atoms present in the lattice. There are always some vacancies…

Q: For a system of particles at room temperature, how large must € - μ be before the Fermi-Dirac,…

A: We know that Boltzmann distribution lies between Bose-Einstein and the Fermi-Dirac distributions. It…

Q: In Maxwell-Boltzmann statistics the particles of an assembly are considered distinguishable, and…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: The probability of finding an N2 molecule at ambient temperature at 515 m/s is zero. True or…

A: Required : True or False : The probability of finding an N2 molecule at ambient temperature at 515…

Question

100%

Obtain the expression for the average thermal energy when the partition function is
Z:
ħo
(A) 극청고
2
(B) kzT
1
(C) -k,T
4
(D) 4k,T

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

If levels 1 and 2 are separated by an energy E2 – E1 such that the corresponding transition frequency falls in the middle of the visible range, calculate the ratio of the populations of the two levels in thermal equilibrium at room temperature and hence interpret the results physically?
Assume a flat Friedmann-Robertson-Walker universe, dominated by a fluid with equation of stateP = c^2 wρ, where the equation of state parameter w is a constant.a) Calculate ρ(a), the dependence of the energy density ρ on the scale factor a b)Determine the value of the equation of state parameter w that gives rise to a scale factorevolution a(t) ∝ t.
P2D.8 Use the fact that (∂U/∂V)T = a/Vm2for a van der Waals gas (Topic 1C)to show that μCp,m ≈ (2a/RT) − b by using the definition of μ and appropriaterelations between partial derivatives. Hint: Use the approximation pVm ≈ RTwhen it is justifiable to do so.
In the canonical ensemble, we control the variables T, p, and N, and the fundamental function is the Gibbs free energy (G). But if we control T, p, and μ, then we will have a different fundamental function, Z (This is the case for cells that often regulate their temperature, pressure, and chemical potentials to maintain equilibrium). Which of the below options should the Z function equal? H - TS - μN H + TS + μN H + TS - μN G + μN F - pV - μN -H + TS + μN
Using the method of the preceding problem, estimate the fraction of nitric oxide (NO) molecules at a temperature of 250 K that have energies between 3.451021 J and 3.501021 J. `
(a) Repeat Exercise 31.2, and convert the energy to joules or calories. (b) If all of this energy is converted to thermal energy in the gas, what is its temperature increase, assuming 50.0 cm3 of ideal gas at 0.250atm pressure? (The small answer is consistent with the fact that the energy is large on a quantum mechanical scale but small on a macroscopic scale.)
Calculate the threshold frequency of Gold with 7.8x10^-19 J Work Function.
Show that heat is a path function.
Imagine a photon gas at inital temperature of T=100K . What is the temperature of the photon gas after it has undegone a reversible adiabatic expansion to 4 times its original volume ? a) 63K b) 400K c) 100K d) 37K
The highest building in Montreal is the ‘1 square building’, with a height of 203m. The atmospheric pressure in the streets of Montreal is P1 = 9.9 x 104 Pa. Suppose air density is constant : ρair = 1,2 kg/m3 and g = 9.8 m/s2. Suppose the rooftop temperature to be T = 298K, and the air composition is 100% N2 molecules. d. How would you find the probability for a molecule picked randomly to have a speed in the range vrms and vrms+5.0 m/s. (No calculations needed) e. Find the ratio between the most probable speed (vmp) and the mean speed (vmean). The collision cross-section of N2 molecules is 0.43 nm2. f. Find the collision frequency. Is it in the order of magnitude that you were expecting? Now, consider Earth's atmosphere as 80% N2 and 20% O2. (No calculations needed) g. Explain if larger, smaller, or equal to the previous situation: - Ratio vmp/vmean - The rms speed vrms - Probability to find a molecule at a speed between vrms and vrms+5.0 m/s. - Collision frequency.
3. Derive a simple expression for the partition function of a simple harmonic oscillator of angular frequency ω at a temperature T.
Consider two immiscible liquids such as water and oil. If a spherical oil molecule of radius r is taken out of the oil phase and placed in the water phase, the unfavorable energy of this transfer is proportional to the area of the solute (oil) molecule newly exposed to the solvent (water) multiplied by the interfacial energy, i, of the oil-water interface. The interfacial energy of the bulk cyclohexane-water interface is i = 50 mJ m-2, and the radius of a cyclohexane molecule is 0.28 nm. Using Boltzmann distribution, estimate the solubility of cyclohexane in water at 25 C in units of mol L-1.The concentration of water in water phase is 55.5 mol L-1.