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Consider the semiclassical model of N particles with two energy levels (0 and e > 0). Suppose that the volume of the gas may be introduced by the assumption that the energy of the excited level depends on V = a e = e(v) vr' E = where a and y are positive constants. Use the fact that the number of microscopic states of the system is given by: N! N! N(E, N) : N4! (N – N,)! (E/e)! (N – E /e)! Obtain an equation of state for the pressure, p = p(T,v), and an expression for the isothermal compressibility (note that the constant y plays the role of the Grüneisen parameter of the solid). Again, as e = :E(v), we can write s = s(u, v). From the equations of state, it is easy to write the isothermal compressibility.

Consider the semiclassical model of N particles with two energy levels (0 and e > 0). Suppose that the volume of the gas may be introduced by the assumption that the energy of the excited level depends on V = a e = e(v) vr' E = where a and y are positive constants. Use the fact that the number of microscopic states of the system is given by: N! N! N(E, N) : N4! (N – N,)! (E/e)! (N – E /e)! Obtain an equation of state for the pressure, p = p(T,v), and an expression for the isothermal compressibility (note that the constant y plays the role of the Grüneisen parameter of the solid). Again, as e = :E(v), we can write s = s(u, v). From the equations of state, it is easy to write the isothermal compressibility.

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter28: Quantum Physics
Section: Chapter Questions
Problem 39P
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Consider the semiclassical model of N particles with two energy levels (0 and e > 0). Suppose that the volume of the gas may be introduced by the assumption that the energy of the excited level depends on V = a e = e(v) vr' E = where a and y are positive constants. Use the fact that the number of microscopic states of the system is given by: N! N! N(E, N) : N4! (N – N,)! (E/e)! (N – E /e)! Obtain an equation of state for the pressure, p = p(T,v), and an expression for the isothermal compressibility (note that the constant y plays the role of the Grüneisen parameter of the solid). Again, as e = :E(v), we can write s = s(u, v). From the equations of state, it is easy to write the isothermal compressibility.
Transcribed Image Text:Consider the semiclassical model of N particles with two energy levels (0 and e > 0). Suppose that the volume of the gas may be introduced by the assumption that the energy of the excited level depends on V = a e = e(v) vr' E = where a and y are positive constants. Use the fact that the number of microscopic states of the system is given by: N! N! N(E, N) : N4! (N – N,)! (E/e)! (N – E /e)! Obtain an equation of state for the pressure, p = p(T,v), and an expression for the isothermal compressibility (note that the constant y plays the role of the Grüneisen parameter of the solid). Again, as e = :E(v), we can write s = s(u, v). From the equations of state, it is easy to write the isothermal compressibility.
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