Practice Problems from Chapter 1-3
Problem 1
V
V2
V1
3
2
1
T1
T2 T
One mole of a monatomic ideal gas goes through a
quasistatic three-stage cycle (1-2, 2-3, 3-1) shown in
the Figure. T1 and T2 are given.
(a) (10) Calculate the work done by the gas. Is it
Lecture 10. Heat Engines and refrigerators (Ch. 4)
A heat engine any device that is capable of converting thermal
energy (heating) into mechanical energy (work). We will consider
an important class of such devices whose operation is cyclic.
Heating the tr
Lecture 11. Real Heat Engines and
refrigerators (Ch. 4)
Stirling heat engine
Internal combustion engine (Otto cycle)
Diesel engine
Steam engine (Rankine cycle)
Kitchen Refrigerator
Carnot Cycle
- is not very practical (too slow), but operates at the maxim
Lecture 13. Thermodynamic Potentials (Ch. 5)
So far, we have been using the total internal energy U and, sometimes, the
enthalpy H to characterize various macroscopic systems. These functions are called
the thermodynamic potentials: all the thermodynamic
Lecture 14. More on Thermodynamic Potentials
Potential
Variables
U (S,V,N)
S, V, N
H (S,P,N)
S, P, N
F (T,V,N)
V, T, N
G (T,P,N)
P, T, N
dU (S , V , N ) = T dS PdV + dN
dH (S , P, N ) = T dS + VdP + dN
dF (T , V , N ) = S dT PdV + dN
dG (T , P, N ) = S dT
Lecture 15. Phases of Pure Substances (Ch.5)
Up to now we have dealt almost exclusively with systems consisting of a
single phase. In this lecture, we will learn how more complicated, multiphase systems can be treated by the methods of thermodynamics. The
Lecture 16. The van der Waals Gas (Ch. 5)
Nobel 1910
The simplest model of a liquid-gas phase
transition - the van der Waals model of
real gases grasps some essential
features of this phase transformation.
(Note that there is no such transformation
in the
Lecture 19. Boltzmann Statistics (Ch. 6)
We have followed the following logic:
1. Statistical treatment of isolated systems: multiplicity entropy the 2nd Law.
2. Thermodynamic treatment of systems in contact with the heat reservoir the
minimum free energy
Lecture 2 The First Law of
Thermodynamics (Ch.1)
Outline:
1. Internal Energy, Work, Heating
2. Energy Conservation the First Law
3. Quasi-static processes
4. Enthalpy
5. Heat Capacity
Internal Energy
The internal energy of a system of particles, U, is the
Lecture 20. Continuous Spectrum, the Density of States
(Ch. 7), and Equipartition (Ch. 6)
Typically, its easier to work with the integrals rather than the sums. Thus, whenever
we consider an energy range which includes many levels (e.g., when kBT > inter-
Lecture 3. Combinatorics, Probability and
Multiplicity (Ch. 2 )
Combinatorics and probability
2-state paramagnet and Einstein solid
Multiplicity of a macrostate
Concept of Entropy (next lec.)
Directionality of thermal processes
(irreversibility)
Ove
Lecture 4. Entropy and Temperature (Ch. 3)
In Lecture 3, we took a giant step towards the understanding why certain
processes in macrosystems are irreversible. Our approach was founded
on the following ideas:
Each accessible microstate of an isolated syst
Lecture 5: 2nd and 3rd Laws of Thermodynamics
An isolated system, being initially in a non-equilibrium state, will evolve
from macropartitions with lower multiplicity (lower probability, lower
entropy) to macropartitions with higher multiplicity (higher p
Lecture 6. Entropy of an Ideal Gas (Ch. 3)
Today we will achieve an important goal: well derive the equation(s) of state
for an ideal gas from the principles of statistical mechanics. We will follow the
path outlined in the previous lecture:
Find (U,V,N,.
Lecture 7. Thermodynamic Identities (Ch. 3)
S (U ,V , N ) k B ln (U ,V , N )
S
S
S
dS =
dU +
dV +
dN
U N ,V
V N ,U
N U ,V
1
S
=
U V , N T
P
S
=
V U , N T
S
=?
N U ,V
Diffusive Equilibrium
and Chemical Potential
UA, VA, NA UB, VB,
Lecture 8. Systems with a Limited Energy Spectrum
The definition of T in statistical mechanics is
consistent with our intuitive idea of the
temperature (the more energy we deliver to a system,
the higher its temperature) for many, but not all
systems.
1
Physics 351
Thermal Physics
Final Exam
Date: 5/8/2012
There are 6 problems. Do all of them. Show all your work. Cross things
out neatly, DO NOT ERASE.
This is a closed textbook exam. You are allowed two sheets of 8.5 11
paper with your notes. Write your n
Thermal Physics = Thermodynamics + Statistical Mechanics
- conceptually, the most difficult subject of the undergraduate
physics program.
Thermodynamics provides a framework of relating the
macroscopic properties of a system to one another. It is
concerne