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(4) Partition function of ideal gas comprising N particles of mass m in potential V(r) in equilibrium at constant temperature T (or ẞ = 1/kT) is given by the following:* Z = 1 3N/2 m d³r N! 2лh²ß Let us consider this ideal gas confined in a box 0 ≤ x ≤ L; 0 ≤ y ≤ L; ho ≤ z≤h₁, and in potential V(x, y, z) = mgz (i.e. uniform gravity). (a) Calculate the partition function and Helmholtz free energy F(B, L, ho, h₁). (b) Calculate the pressures at the bottom and the top of the box, po and P₁. (c) Calculate the heat capacity Cy. Your answer should be different from 3/2R of the monoatomic ideal gas. Consider a realistic measurement (such as the size of the box) of the heat capacity using argon gas (molecular weight = 40 [g/mol]), and describe how the difference between your calculated Cy and ³/2R can be reconciled. *h is a number but no knowledge is needed. It's called "Planck's constant" (see lecture notes).

(4) Partition function of ideal gas comprising N particles of mass m in potential V(r) in equilibrium at constant temperature T (or ẞ = 1/kT) is given by the following:* Z = 1 3N/2 m d³r N! 2лh²ß Let us consider this ideal gas confined in a box 0 ≤ x ≤ L; 0 ≤ y ≤ L; ho ≤ z≤h₁, and in potential V(x, y, z) = mgz (i.e. uniform gravity). (a) Calculate the partition function and Helmholtz free energy F(B, L, ho, h₁). (b) Calculate the pressures at the bottom and the top of the box, po and P₁. (c) Calculate the heat capacity Cy. Your answer should be different from 3/2R of the monoatomic ideal gas. Consider a realistic measurement (such as the size of the box) of the heat capacity using argon gas (molecular weight = 40 [g/mol]), and describe how the difference between your calculated Cy and ³/2R can be reconciled. *h is a number but no knowledge is needed. It's called "Planck's constant" (see lecture notes).

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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(4) Partition function of ideal gas comprising N particles of mass m in potential V(r) in equilibrium at constant temperature T (or ẞ = 1/kT) is given by the following:* Z = 1 3N/2 m d³r N! 2лh²ß Let us consider this ideal gas confined in a box 0 ≤ x ≤ L; 0 ≤ y ≤ L; ho ≤ z≤h₁, and in potential V(x, y, z) = mgz (i.e. uniform gravity). (a) Calculate the partition function and Helmholtz free energy F(B, L, ho, h₁). (b) Calculate the pressures at the bottom and the top of the box, po and P₁. (c) Calculate the heat capacity Cy. Your answer should be different from 3/2R of the monoatomic ideal gas. Consider a realistic measurement (such as the size of the box) of the heat capacity using argon gas (molecular weight = 40 [g/mol]), and describe how the difference between your calculated Cy and ³/2R can be reconciled. *h is a number but no knowledge is needed. It's called "Planck's constant" (see lecture notes).
Transcribed Image Text:(4) Partition function of ideal gas comprising N particles of mass m in potential V(r) in equilibrium at constant temperature T (or ẞ = 1/kT) is given by the following:* Z = 1 3N/2 m d³r N! 2лh²ß Let us consider this ideal gas confined in a box 0 ≤ x ≤ L; 0 ≤ y ≤ L; ho ≤ z≤h₁, and in potential V(x, y, z) = mgz (i.e. uniform gravity). (a) Calculate the partition function and Helmholtz free energy F(B, L, ho, h₁). (b) Calculate the pressures at the bottom and the top of the box, po and P₁. (c) Calculate the heat capacity Cy. Your answer should be different from 3/2R of the monoatomic ideal gas. Consider a realistic measurement (such as the size of the box) of the heat capacity using argon gas (molecular weight = 40 [g/mol]), and describe how the difference between your calculated Cy and ³/2R can be reconciled. *h is a number but no knowledge is needed. It's called "Planck's constant" (see lecture notes).
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