specific.3- a) Show that the entropy of the system in the grand canonical ensemble can be written as S =-kE, P,lnP,.b) Assuming that the total number of microstates accessible to a given statistical system is N, showthat the entropy of the system in part (a) is maximum when all n states are equally likely to occur.c) If, on the other hand, we have an ensemble of systems sharing energy (with mean value E), thenshow that the entropy, as given by the same formal expression, is maximum when P, oxe-BEr, Bbeing a constant to be determined by the given value of E.d) Further, if we have an ensemble of systems sharing energy (with mean valueË) and also sharingparticles (with mean value N), then show that the entropy, given by a similar expression, ismaximum when Ps xe-aNr-BEs, a and B being constants to be determined by the given valuesof N and E.

Answered: stem in part (a) is re have an ensemble

Science

Chemistry

stem in part (a) is re have an ensemble

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

See similar textbooks

Related questions

Q: QUESTION 2 a) Distinguish between spherical rotors and symmetrical rotors in terms of numbers of…

A: e) Derivation of the Sackur-Tetrode Equation:The Sackur-Tetrode equation is an expression for the…

Q: What configurations must undergo the distortions predicted by the Jahn-Teller theorem? Why is…

Q: non a जाज्ना व Jotanced greaption- १ AJ(S) + 3 H3sou(c० ->Hlo. (डoपानुब) + 3h,55) गाए्e फर OCa…

A: Given:: Moles of Al = 1.18 mol moles of H2SO4=1.14 mol Theoretical yield of Al2(SO4)3=?

Q: The unit cel ls of SbCI3 are orthorhombic w ith dimensions a= 812 pm. b = 947 pm. and c = 637 pm.…

A: For orthorhombic system, So that, Where, dkhl=spacing of planes.

Q: Explain why does it require an input of energy when an uncharged molecule moves from a concentration…

A: The movement of molecules from a region of lower concentration to a region of higher concentration…

Q: For the transition: HgS(red) = HgS(black) deltaG°=4100-6.0T. Determine the transition temp in…

Q: Show the symmetry operations for all the symmetry elements present, and determine the transformation…

Q: Compute the rotational constant B, in Joules, of a hydrogen chloride molecule with a Cl isotope…

A: B is the rotational constant, which is related to the moment of inertia.

Q: Within the Hückel approximation, comment on the differences in the secular determinants for the…

Q: give

A: Frank codon explains that transition of the electrons occurs so rapidly that the nuclei are…

Q: Briefly describe the contribution of Walter Nernst, J. W. Richards, Max planck and G.N.Lewis in the…

A: Walther Nernst (1864 – 1941) made a significant breakthrough with his statement of the Third Law of…

Q: The no. Of IR active vibrational normal modes of CO2 are

Q: 1. Calculation of the Average, Percent error, Standard deviation, and Relative standard deviation.…

A: For the given set of data, we have to calculate the average, percent error, standard deviation and…

Q: How is spectrophotometry connected to Beer Lambert's Law. Explain briefly

A: We have to find out the connection between absorbance and Lambert Beers Law

Q: Briefly describe the contributions of Walter Nernst, T. W. Richards, Max Planck and G. N. Lewis in…

A: Walther Nernst (1864 – 1941) made a significant breakthrough with his statement of the Third Law of…

Q: Statistical Thermodynamics show that this relation is valid! Derivation how to get this equation!…

Q: ) What are basis sets? Explain in detail the 6-31G basis set.

Q: potassium can be determined by flame emission spectroscopy using an internal lithium standard

A: Potassium can be determined by flame emission spectrometry (flame photometry) using a lithium…

Q: The number of expected vibrations of CH3CH2CH2Br (nonlinear molecule) are: *

Q: In which part of the UV-Visible spectrum are these - * excitations expected to be observed?

A: To describe in which part of UV-Vis spectrum does the given π→π* transitions occur.

Q: What is the symmetry element corresponding to (a) Cn, (b) s, (c) i, (d) Sn?

Q: 1,3,5-heptatrienyl radical (an open chain of seven carbon atoms) has the following roots for the…

A: a) The value of Energy is given by: E=α-xβ Determination of energy at different values of x:…

Q: 1. Properties of gases Determine the molecular mass M , specific gas constant R, mass-specific…

A: In the given question we have to calculate the molecular mass, specific gas constant, and…

Q: A material has two energy levels with a separation of 2.1eV. At what temperature will the upper…

A: The ratio of the population of two energy state of an atom is given by N2N1=e-ΔEKT Where, N2 is the…

Q: Noise is a result of which source(s): Filtering Diffraction of Radiation O Shielding Chemical O…

A: NOISE: Noise is defined as an unwanted sound which is very loud or unpleasant. It can be created by…

Q: Explain, based on the equations of Beer's Law and its equivalent for fluorescence, why increasing…

A: The objective of this question is to show the increasing light intensity is more useful for…

Q: Q4: Derive planar density expressions for BCC (100) and (110) planes in terms of the atomic radius…

A: (1,0,0) plane within a BCC unit cell si given below.

Q: How do we come to know that Dirac equation deals with half spin? Discuss it in detail.

A: Answer- Dirac equation -

Q: deduce the symmetries of the vibrations for phosgene

Q: Use Appendix data and the ap mate AH200 for the reaction 2C0(.

A: Enthalpy is defined as the energy of a thermodynamic system. It is mathematically defined as the sum…

Q: 5- The vibrations in infrared spectroscopy might be active or inactive?

A: IN order for a vibrational mode to absorb infrared light, it must result in a periodic change in the…

Q: For a diatomic vibrating rotor, in vibrational level v =3 and rotational level J, the sum of the…

A: Given that the sum of rotational and vibrational energies is 11493.6cm-1. Equlibrium frequency is…

Q: Imagine a system in local thermal equilibrium at temperature T which contains both massless spin-1/2…

A: In local thermal equilibrium, the energy density of a system can be expressed as the sum of the…

Q: If the second-lowest energy level of a system is separated from the ground state by 0.5kBT, what…

Q: Provide brief definitions of fluorescence and phosphorescence, with aid of a Jablonski diagram.

A: Photochemistry via branch of chemistry that deals with study of interaction of radiations with…

Q: Bb MYJCC Blackboard Learn WebAdvisor for Students JCC Self Service Bb UTF-8 Syllabus_CHM%20151%2 X A…

A: As per regulations, only three sub-parts can be answered.

Q: If the hydrogens labeled 'a' integrate for H, what integration is found for the hydrogens labeled…

Q: The force constants for ¹H₂ and 79Br₂ are 575 and 246 N-m-¹, respectively. The atomic masses for ¹H₂…

A: Given,The force constant of H2= 575 N/mThe force constant of Br2 =246 N/mTo find the vibrational…

Q: For each figure determine if the encounter is successful or unsuccessful and describe what you are…

A: Given: We are provided with potential energy diagrams through which we have to decide whether the…

Q: How to determine symmetry elements, σh and σν and how to differentiate between both. Also , how is…

A: To determine the symmetry operation, reflect a element on a mirror plane, rotate a molecule along…

Q: 1. What is the theorem of "equipartition of energy" in classical statistical mechanics? Based on…

Q: Provide brief definitions of fluorescence and phosphorescence, with aid of a Jablonski diagram

Question

specific.
3- a) Show that the entropy of the system in the grand canonical ensemble can be written as S =
-kE, P,lnP,.
b) Assuming that the total number of microstates accessible to a given statistical system is N, show
that the entropy of the system in part (a) is maximum when all n states are equally likely to occur.
c) If, on the other hand, we have an ensemble of systems sharing energy (with mean value E), then
show that the entropy, as given by the same formal expression, is maximum when P, oxe-BEr, B
being a constant to be determined by the given value of E.
d) Further, if we have an ensemble of systems sharing energy (with mean valueË) and also sharing
particles (with mean value N), then show that the entropy, given by a similar expression, is
maximum when Ps xe-aNr-BEs, a and B being constants to be determined by the given values
of N and E.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 3 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, chemistry and related others by exploring similar questions and additional content below.

Similar questions

Q5. For CO2, the bending vibrations are of symmetry type, ay (a) A1g, +4² (Log (6) The Xc) Et (d) Azu
Explain the orig in of the Franck-Condon principle and how it leads to the appearance of vibrational structure in an electronic transition.
16 The figure depicted below is for Ritipenem structure, which is an antimicrobial agent, and its H-NMR spectrum (labile protons like OH and NH are not shown). What is the multiplicity of the peak corresponding to protons at carbon (h)? OH NH OH (4) (1) (5) 3) (2) Chemiral in A Triplet Quintet Other Singlet Quartet Doublet
For a specific molecule the ground state is nondegenerate while the first excited state is doubly degenerate. The excited state is removed from the ground state by 380 cm-1. What must the temperature of the system be for i) 25% and ii) 45% of the molecule to be in the first excited state?
Please answer this question. Thank you.
If the hydrogens labeled 'a' integrate for ¹H, what integration is found for the hydrogens labeled 'b'? O O 1H 2H 3H 4H 5H ng to another question will save this response. a b
Use the equipartition principle to estimate the value of γ = Cpm/CVm for gaseous N2O5. Do this calculation WITH the vibrational contribution to the energy. a. 1.07 b. 1.33 c. 1.4 d. 1.7 e. 1.5
What is the evaluation for the coefficient x, y, z in equalizable?
Explain the differences between semi-empirical and ab initio methods of electronic structure computation.
Ə In q rot to derive the rotational contribution to the energy for a Use the equation Eo1 = NKT² ƏT diatomic molecule
Give a clear explanation handwritten answer.....
Indicate if they are true or false and give a brief explanation. - The probability of spontaneous emission depends on the population of the initial excited level - The intensity of light absorbed by a molecule increases with the energy it has.