Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 38, Problem 65P
To determine
Show that the average energy at
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Question 2:
Suppose a solid contains 3 identical independent one dimensional oscillstors and sar
i.e. 0, 1 and 2, then-
he only the ee td mer
O there is only one macrostate with total energy zero.
o there are two macrostates with total energy zero.
O There are nine macrostates with total energy zero.
O There are three macrostates with total energy zero.
The effective mass of the solid whose energy expression &(k)= A- Bcos (k,b) cos(k,b)
(0'0) is equal to,
near
One description of the potential energy of a diatomic molecule is given by the Lennard–Jones potential, U = (A)/(r12) - (B)/(r6)where A and B are constants and r is the separation distance between the atoms. Find, in terms of A and B, (a) the value r0 at which the energy is a minimum and (b) the energy E required to break up a diatomic molecule.
Chapter 38 Solutions
Physics for Scientists and Engineers, Vol. 1
Ch. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10P
Ch. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46PCh. 38 - Prob. 47PCh. 38 - Prob. 48PCh. 38 - Prob. 49PCh. 38 - Prob. 50PCh. 38 - Prob. 51PCh. 38 - Prob. 52PCh. 38 - Prob. 53PCh. 38 - Prob. 54PCh. 38 - Prob. 55PCh. 38 - Prob. 56PCh. 38 - Prob. 57PCh. 38 - Prob. 58PCh. 38 - Prob. 59PCh. 38 - Prob. 60PCh. 38 - Prob. 61PCh. 38 - Prob. 62PCh. 38 - Prob. 63PCh. 38 - Prob. 64PCh. 38 - Prob. 65PCh. 38 - Prob. 66PCh. 38 - Prob. 67PCh. 38 - Prob. 68PCh. 38 - Prob. 69PCh. 38 - Prob. 70PCh. 38 - Prob. 71PCh. 38 - Prob. 72PCh. 38 - Prob. 73PCh. 38 - Prob. 74PCh. 38 - Prob. 75PCh. 38 - Prob. 76P
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
- 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.arrow_forwardPlease answer the ff and show the step by step solution including its units:arrow_forwardOne model that is used for the interactions between animals, including fish in a school, is that the fish have an energy of interaction that is given below by a Morse potential. The fish will attract or repel each other until they reach a distance that minimizes the function V(r). The coefficients A and a are positive numbers. Complete parts (a) through (c). V(r)=e^-r -Ae^-ar, r>0 Find the value of r that minimizes V(r).arrow_forward
- Consider the Lennard-Jones potential between atoms of mass m in a solid material. a) Find the dependence of the equilibrium position r0 on the parameters in the potential. b).For small perturbations, δr around r0, determine the restoring force as a function of δr and as a result determine the natural frequency ω0 of oscillation of the atoms as a function of the coefficients in the Lennard-Jones potential.arrow_forwardWhat is the formula for the fluctuation in the (internal) energy of a system Oy? Prove by direct differentiation and using Ə (log Z)| U = kgT² ƏT that the fluctuation in the energy is given by the following formula: of = kgT². ƏT V,Narrow_forwardGlasses are materials that are disordered – and not crystalline – at low temperatures. Here is a simple model. Consider a system with energy E, the number of accessible microstates is given by a Gaussian function: Ω(E) = Ω0 e −(E−E¯) 2/(2∆2 ) , where Ω0 and E¯ and ∆ are positive constants. E¯ is the average energy. In this problem, we consider only the states whose energy E is below E¯. 1. Show that the entropy is an inverted parabola: S(E) = S0 − α (E − E¯) Find S0 and α. Write your answers in terms Ω0, ∆, and other universal constants. 2. An entropy catastrophy happens when S = 0, which occurs at energy E0. (i) Find E0. (ii) What is the number of accessible states for energy below E0? 3. The glass transition temperature Tg is the temperature of entropy catastrophy. Compute Tg. 4. Find the energy E as a function of T. 5. Without any calculation, explain why E → E¯ as T → +∞. Hint: consider the Boltzmann distributionarrow_forward
- The binding energy of an electron in a hydrogen atom is 13.6 electron volts. At what temperature will the hydrogen atom’s adiabatic index start to rise, due to the electron and proton being two particles?arrow_forwardS/sng Hooki Law , and throught the given Values Find the Value of the Constant K and then draw the dagram. X (mm) 20 2 30 21 40 32 3 44 54 67 92 115 50 60 6 70 110 138 161 130 150 lo 14. 200 226arrow_forwardQ/A particle of mass m moves in one dimension according to the potential energies . (a) V(æ)= a² + %3D (b) V(x) = kxe-bz (c) V (x) = k(xª – b²x²) %3D Find the equilibrium position for each state and test its stability?arrow_forward
- One model that is used for the interactions between animals, including fish in a school, is that the fish have an energy of interaction that is given below by a Morse potential. The fish will attract or repel each other until they reach a distance that minimizes the function V(r). The coefficients A and a are positive numbers. Complete parts (a) through (c). V(r)=e^-r -Ae^-ar, r>0 a) assume initially that a=1/2 and A=1 what is the behavior of V(r) as r approaches 0arrow_forwardOne model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is U(r) = U₁[(¹)¹² – ()] where ro = 0.8 nm and ₹₁ = 6.1 eV. 19 Note: 1 eV = 1.6 × 10-¹⁹ J. Some helpful units: [Force] = eV/nm [Energy] = eV [distance] = nm Equilibrium Distance What is the distance between the atoms when the molecule is in stable equilibrium? Click here for a hint req Hint: Hint: Hint: Hint: Hint: Force If the distance between the atoms increases from equilibrium by r₁ = 0.35 nm, then what is the force from one atom on the other associated with this potential energy? (Enter your answer as postive if they repel each other, and negative if they attract.) Fr(req+r₁) Hint: 0.89105934nm Hint:arrow_forward[ 2- j4 YBus = -1+ j3 |-1+ j3 3.6 – j10 -1+ j3| pu -1+ j3 -2 + j3] V, = 1.0122° V2 P +jQ1 0.2 – j0.3 1+ j0.4 Figure 3 a) With the complex power on buses 2 and 3 as shown in the figure, determine the values for V, and V3 produced by the first iteration of the Gauss-Seidel procedure.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning