Statistical Thermodynamics Problems and Solutions

Assignment Help in Statistical Thermodynamics

Created bySusan Tayfe

Last updated 5/2026

English

What you'll learn

Problem solving skills in Statistical Thermodynamics
Having access to the step by step solutions of problems in Statistical Thermodynamics
Reviewing the rules of Statistical Thermodynamics while applying them to the problems
Preparing for the exam in Statistical Thermodynamics

Course content

5 sections • 16 lectures • 1h 37m total length

Maxwell’s Four Thermodynamic Relations11:02
In this lecture you will derive Maxwell's four relations from four thermodynamic potential functions, U, H, F, G for closed systems. Where U is internal energy, H is enthalpy, F is Helmholtz free energy, and G is Gibbs free energy of the systems. An image of this question is available in Downloadable Resources.
Equations Between Heat Capacities at Constant Pressure and Constant Volume8:47
Proof of two different expressions of heat capacity at constant pressure minus heat capacity at constant volume (C_P-C_V). An image of this question is available in Downloadable materials.
Rate of Change of Heat Capacity with Volume4:46
This lecture is the step by step solution of the following question:
Question: Find a general expression for the rate of change of C_V (heat capacity at constant volume) with volume at constant temperature T. Then evaluate this expression for a van der Waals gas. An image of this question is available in Downloadable materials.
Rate of Change of Heat Capacity of Rubber Band with Length8:31
This lecture is the step by step solution of the following question:
Suppose a particular type of rubber band has the EoS of L=Af/T, where L is the length of rubber band, f is the tension, T is the temperature, and A is a constant. For this system compute compute partial derivative of C_L with respect to L at constant T, where C_L is the constant length heat capacity. An image of this question is available in Downloadable materials.
Chemical Potential of Rubber Band3:39
This lecture is the step by step solution of the following question:
Suppose an equation of state for a rubber band is U=θS^2L/n^2, where θ is a constant, L is the length of the rubber band, n is a mole number of the rubber band, and S is an entropy of the rubber band. The First Law of Thermodynamics for this system can be written as, dU = T dS − f dL + µdn
where f is a tension of the rubber band. Determine the chemical potential as a function of T and L/n.
An image of this question is available in Downloadable materials.

Expansion of Argon as a Van der Waals Gas5:29
In this lecture the following question is solved step by step:
Question: Argon can be described by Van der Waals equation of state. 2 moles of argon gas are expanded reversibly and isothermally from 3 L to 8 L at 27 degrees Celsius. Calculate the work (in Jules) done by the gas during this expansion. An image of this question is available in Downloadable materials.
Transition of a Gaseous System Through a Parabola7:39
This lecture is the step by step solution of the following problem:
Question: For a particular gaseous system it has been determined that energy is given by:
U = 2.5 P V + constant
In this equation P is expressed in Pascal and V is in m3 . The system is initially in the state A (P=0.2MPa, and V=10 L). The system is then
transferred to the state B (P=0.2MPa, V=30 L) along the parabola
P = 10^5 + 10^3 (V − 20)^2
In this equation volume is in liters and pressure is in Pascals. Calculate Q and W for this process. Also find the equation of the adiabats in the P-V plane (i.e., find the form of the curves P=P(V) such that δQ = 0 along the
curves). An image of this question is available in Downloadable materials.
Isothermal Expansion of Van der Waals Gas and Ideal Gas8:53
This lecture is the solution of the following question:
Question: Evaluate ∆U and ∆S for isothermal expansion from volume V1 to volume V2 (V2 > V1 ) of one mole of ideal gas and one mole of van der Waals gas. Compare and rationalize the differences. An image of this question is available in Downloadable materials.

Canonical Ensemble: Variance in Energy3:20
This lecture is the proof of the equation between variance of the energy and partial derivative of average energy with respect to β at constant volume in canonical ensemble.
You can find an image of question in Resources.
Grand Canonical Ensemble: Variance in Number of Particles4:26
This lecture is the proof of the equation between variance of the number of particles and partial derivative of expected value of number of particles with respect to βµ at constant volume in grand canonical ensemble.
You can find an image of question in Resources.
A Molecule at Two Energy Levels5:33
This lecture is the solution of the following question:
A molecule can be found at two levels with energies 0 and 300 cm^-1 . What is the probability to find the molecule at upper level at temperature 250^o C?
You can find an image of question in Resources.
Partial Differential Equation between Grand Energy and Average Pressure4:10
This lecture is the solution of a problem available in downloadable resources.

Maximizing Entropy Subject to Constraint on Probabilities4:53
This lecture is the step by step solution of the following question:
Use the method of undetermined multipliers to show that entropy subject to constraint that the sum of probabilities of microstates is equal to one, is maximum, when all of the microstates have the same probability of 1/N.
You can find an image of question in Resources.
Maximizing Entropy Subject to Constraint on Probabilities and Energies5:01
This lecture is the step by step solution of the following question:
Maximize entropy, subject to the constraints that the sum of probabilities of micro-states is equal to one, and average of micro-states energies is U.
You can find an image of question in Resources.

Requirements

Calculus and fundamentals of physics

Description

This course is created tor the college students who need help with their assignments in statistical thermodynamics. In this course I have provided step by step solutions while explaining the rules of statistical thermodynamics. So in addition to the solutions of problems, you will review the rules of statistical thermodynamics and how you can apply the rules to problems.

In order to join to this course, you need to be familiar with differential equations and integrals and know the fundamentals of physics.

I will add more solutions to this course in the future, meanwhile students are welcomed to ask any question they may have about the published solutions or if they need help with any other problems in statistical thermodynamics, or to share their comments about this course that will help me to improve the course.

This course is made of the following sections:

Statistical Thermodynamic Quantities and Equations: problems and solutions about deriving equations between statistical thermodynamic quantities and applying them to the problems.
Thermodynamic Processes: problems and solutions where first law of thermodynamics, equations of state, work done by the gas, internal energy, and heat transfer are discussed.
Partition Functions and Ensembles: problems and solutions involving partition functions in different ensembles.
Lagrange Undetermined Multipliers: problems and solutions about maximizing entropy using Lagrange undetermined multipliers.
Quantum Thermodynamics: Problems and solutions involving quantum systems where statistical thermodynamics rules are applicable.

Register to this course and enjoy solving problems in statistical thermodynamics while reviewing the subject itself through well-explained step by step solutions!

Who this course is for:

Students

Statistical Thermodynamics Problems and Solutions

What you'll learn

Explore related topics

Course content

Statistical Thermodynamic Quantities and Equations5 lectures • 37min

Thermodynamic Processes3 lectures • 22min

Partition Functions and Ensembles4 lectures • 17min

Lagrange Undetermined Multipliers2 lectures • 10min

Quantum Thermodynamics2 lectures • 11min

Requirements

Description

Who this course is for: