Concepts.doc (Word 97)


Note: This list is only a guide to help you study. It is NOT comprehensive, and the exam may cover any topics discussed in class.

Equations of State


PV = nRT

Van der Waals

First Law of Thermodynamics

For an irreversible expansion against a constant external pressure

For an isothermal reversible expansion,

At constant volume, w = 0; if there is no non-expansion work, then

  • Other Topics: thermochemistry


At constant pressure (with no non-expansion work),

Joule Experiment

  • Expansion into a vacuum
  • Joule tried to measure the change in temperature with volume at constant U;
  • No work was done because the gas was expanding against a vacuum (Pext = 0, w = 0)
  • For an ideal gas, the temperature will not change because no work is done. For a real gas, the temperature will decrease slightly (although Joule was not able to measure any change in temperature because his equipment was not sensitive enough)
  • For an ideal gas, mJ = 0

Joule-Thomson Experiment

  • Expansion at constant H (isenthalpic)
  • A gas at high pressure expands through a throttle valve into an area of lower pressure. The container is insulated so that the expansion is adiabatic.
  • For an ideal gas, mJ-T = 0
  • For real gases, the Joule-Thomson coefficient is a property of the material that depends on temperature and pressure.
  • The Joule-Thomson inversion temperature is the temperature above which mJ-T is negative, and below which mJ-T is positive. When mJ-T is negative, the gas will warm upon expansion. When mJ-T is positive, the gas will cool upon expansion.

Heat Capacities

At constant volume,

At constant pressure,

Second Law of Thermodynamics


For an ideal gas:

For mixing, the total entropy change is

and the entropy change per mole of mixture is

For a reversible adiabatic process, DS = 0

Maxwell Relations

Isothermal Compressibility

Coefficient of Thermal Expansion



Criteria for spontaneity

At constant P and T DG < 0

At constant V and T DA < 0

At constant V and S DU < 0

At constant P and S DH < 0

Other Concepts

  • State vs. path functions
  • Exact vs. inexact differentials; Euler's Relation
  • Reversible vs. irreversible processes
  • Open, closed, isolated systems; homogeneous vs. heterogeneous systems; singular vs. compound systems; partitioned systems; etc.
  • Different types of processes: isothermal, isopiestic (isobaric), isochoric, isoenthalpic, isoentropic, adiabatic
  • Equipartition of energy, how it is used to predict energies and heat capacities
  • Boltzman expression
  • Critical V, P, T
  • Carnot Cycle
  • Clausius Inequality
  • Third Law of Thermodynamics

Relevant pages in Mortimer are up to and including Section 5.2.

Note: This list is only a guide to help you study. It is NOT comprehensive, and the exam may cover any topics discussed in class.