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Prove that, for any system in equilibrium with a reservoir

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder ISBN: 9780201380279 40

Solution for problem 16P Chapter 6

An Introduction to Thermal Physics | 1st Edition

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An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

An Introduction to Thermal Physics | 1st Edition

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Problem 16P

Problem 16P

Prove that, for any system in equilibrium with a reservoir at temperature T, the average value of the energy is

where β = 1/kT. These formulas can be extremely useful when you have an explicit formula for the partition function.

Step-by-Step Solution:
Step 1 of 3

L4 4.4 Professor OH M 15-16, W 12-13 Finish operator overloading and start class inheritance Postfix vs. Prefix Fraction& operator++() prefix Increments before all Fraction& operator++(int unused) postfix Stores old value, increments, returns old value Class Inheritance One goal to strive is avoid having redundant code. Class inheritance allows us to exploit commonalities between classes How it works: Create a base class that has features 2+ classes share Create derived classes from the base class. class Derived : public Base { … } public functions of Base = public functions for Derived L5 4.6 Continuing inheritance Protected: allows derived classes access to var/f, but nothing else Animal.h Animal.cpp Animal_example.cpp L6 4.8 Introduce pointers and memory leaking Pass by reference: changing value of passed variable Pass by value: creates new variable with the same value as the passed variable Pointer gives more efficiency in memory as you don’t create new, unnecessary variables Pointer stores address of an object, more flexible Declaration * varName; Dereference a = *a_ptr stores value pointed by a_ptr to a Access functions a_ptr->function() Allocate object using “new” makes object stay in memory until explicitly deleted Functions can help make new objects that stay after function terminates Stack memory: temporary memory; variables declared within functions deleted after function terminates Heap memory: Uses “new”, memory remains at address until explicitly deleted New objects ^ are called dynamic memory allocation Memory Leak When allocated memory is deallocated and there’s no way to access it to delete it. Will lead to crashing because it uses up all resources.

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Chapter 6, Problem 16P is Solved
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Textbook: An Introduction to Thermal Physics
Edition: 1
Author: Daniel V. Schroeder
ISBN: 9780201380279

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Prove that, for any system in equilibrium with a reservoir