Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
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Chapter 38, Problem 65P
To determine
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Question 2:
Suppose a solid contains 3 identical independent one dimensional oscillstors and sar
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O there is only one macrostate with total energy zero.
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O There are nine macrostates with total energy zero.
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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
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- 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
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