Abstract
Physics is arguably unique in its emphasis on constructing models that may pertain to systems of interest. Often, these models are simple and lacks of the complexity of the real systems. But the payoff of such simplicity is the ability to fully predict and understand the model system. The hope always is that such understanding will give insight into the physics of the real system of interest.
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Notes
- 1.
Gas in a more general shaped vessel is analyzed in appendix B. A beneficial payback of that analysis is its agreement with Pascal’s law. From Pascal’s law it can be concluded that in the absence of external, space and direction dependent, forces the pressure of a fluid is constant throughout the vessel.
- 2.
The molecule being considered here is monatomic, that is, a single atom constitutes a molecule.
- 3.
For values of the physical constants, see http://physics.nist.gov/cuu/Constants. Note that the numbers in the parenthesis represent the standard uncertainty corresponding to the last digits shown.
- 4.
As is the case here, there is no interaction!
- 5.
Maxwell, J. Clerk (6/13/1831–11/5/1879); Gibbs, Josiah Willard (2/11/1839)–(4/28/1903); Boltzmann, Ludwig Eduard (2/20/1844)–(9/5/1906).
- 6.
A more complete analysis is given in (11.80)–(11.81).
- 7.
Note, normalized average of any constant, say α, is equal to itself, that is, < α > = α.
- 8.
For example, such as gravity.
- 9.
Different macroscopic parts of a thermodynamic system are in equilibrium. Therefore, they have the same temperature. See, for example, the section on the “Zeroth Law, Revisited” in the chapter titled: “Equilibrium, Motive Forces, and Stability.”
- 10.
Of course, gravity and other external fields are assumed to be absent.
- 11.
See, for example, (4.2) and the description provided in the following parts of that chapter.
- 12.
See the related (7.56) and the associated discussion in the section titled: From Empirical to Thermodynamic Temperature.
- 13.
Carnot, N. L. Sadi (6/1/1796)–(8/24/1832).
- 14.
Boyle, Robert (1/25/1627)–(12/31/1691).
- 15.
Charles, Jacques Alexander César (11/12/1746)–(4/7/1823).
- 16.
Celsius, Anders (11/27/1701)–(4/25/1744).
- 17.
On the Celsius scale, the temperature of the ice-point T is 0 ∘ . Note, the ice-point is represented by the equilibrium state of a mixture of pure water, fully saturated with air at pressure of exactly one atmosphere, and pure ice.
- 18.
The steam-point refers to the equilibrium state of pure water boiling under one atmosphere of air. On the Celsius scale the temperature of the steam-point is set at 100 ∘ .
- 19.
The triple point is where water vapor, pure liquid water, and pure ice all coexist in thermodynamic equilibrium. At this temperature, defined to be exactly equal to 273. 16 K, the sublimation pressure of pure ice equals the vapor pressure of pure water.
- 20.
For this reason, when referring to a gas we shall use the terms “perfect” and “ideal” synonymously.
- 21.
Usually, thermodynamic quantities for one mole will be denoted by lower case subscripts while upper case subscripts will refer to systems of general size. Thus, the specific heat C V is n times the molar specific heat which in turn is denoted as C v . The same applies to C P and C p . While we shall make an effort to follow this rule about the subscripts, often-times, for convenience, C v will equivalently be denoted as c v , and C p as c p . And occasionally – hopefully not often – we may mistakenly even forget to follow this rule!
- 22.
Dalton, John (9/6/1766)–(7/27/1844).
- 23.
When mass M is measured in kg, g in meters/second2, and h in meters, then the dimensions of the numerator of the exponent are: Mgh = kg ×m2/s2 = J.
The denominator, that is, RT, should be considered to be nRT where the number of moles n is equal to 1. Accordingly, the denominator translates into the following units: mol for 1, J K − 1 mol − 1 for R, and K for the temperature T. Thus, the dimensions of the denominator are: mol ×J K − 1 mol − 1 × K = J.
- 24.
Compare (2.57).
- 25.
For a more complete analysis, which also includes calculation of thermodynamic potentials, see (11.100)–(11.108).
- 26.
Compare with (2.31). Indeed, all non-relativistic monatomic ideal gases, whether they be classical or quantum, obey this two-thirds U relationship.
- 27.
“Q.E.D.” stands for the Latin: “Quod Erat Demonstrandum,” meaning “Which Was To Be Proven.”
- 28.
One mole of the abundant isotope contains exactly 12 g of carbon.
- 29.
The mass of one mole of diatomic oxygen is 16 g.
- 30.
Or equivalently, work − ΔW is done by the gas.
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Tahir-Kheli, R. (2012). Perfect Gas. In: General and Statistical Thermodynamics. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21481-3_2
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