Abstract
Much like other scientific disciplines, thermodynamics also has its own vocabulary. For instance, while dealing with objects composed of very large numbers of particles, one might use terms like thermodynamic system; adiabatically isolating, and adiabatically enclosing, walls; adiabatic and nonadiabatic enclosures; conducting and/or diathermal walls; isothermal, isobaric, isochoric, quasistatic, reversible, and irreversible processes; state functions and state variables; thermodynamic equilibrium and, of course, temperature in its various representations.
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Notes
- 1.
By international agreement, the relative atomic mass of \(N_{\mathrm{A}}\) carbon-12 atoms is chosen to be exactly equal to 12. Note that a carbon-12, i.e., 12C6, atom has 6 protons and 6 neutrons. The Avogadro’s number, \(N_{\mathrm{A}}\), is so chosen that the mass of \(N_{\mathrm{A}}\) carbon-12 atoms is exactly equal to 12 g. Measured thus, \(N_{\mathrm{A}}\) is equal to \(6.02214179(30)\times 10^{23}\,{\mathrm{mol}}^{-1}\). References to one mol always specify \(N_{\mathrm{A}}\) particles whether they be atoms or molecules.
- 2.
Note that both carbon and helium molecules are monatomic.
- 3.
Avogadro’s number \(N_{\mathrm{A}}=6.02214179(30)\times 10^{23}~{\text{mol}}^{-1}\).
- 4.
Although we have chosen to represent \(p_{\mathrm{A}}\) as a function of (\(v_{\mathrm{A}}\), \(p_{\mathrm{B}}\), \(v_{\mathrm{B}}\)), any other of these four variables could equally well have been chosen as a function of the remaining three.
- 5.
It bears noting that \(f_{1}(x,y,z)\) and \(f_{2}(x,y,z)\) are, in all likelihood, not the same functions. This is especially true if \(B\) and \(C\) are physically different systems.
- 6.
Note \(f_{3}(x,y,z)\), a function of the three variables \(x,y\), and \(z\), is in all likelihood different from \(f_{1}(x,y,z)\) and \(f_{2}(x,y,z)\) encountered in (1.3).
- 7.
Such an empirical temperature could be defined by any appropriate thermometric property that both systems share.
- 8.
It should be noted that the implications of the zeroth law are not limited to just simple thermodynamic systems. Systems with an arbitrary number of thermodynamic state variables also obey the zeroth law equally well.
- 9.
Note: some authors—e.g., D. ter Haar and H. Wergeland [2]—prefer to use the term total differential.
- 10.
Beginners usually benefit by being reminded that the operation \((\frac{\partial Z}{\partial X})_{\mathrm{Y}}\) consists in finding a derivative of \(Z\) with respect to \(X\) while holding the variable \(Y\) constant.
- 11.
See any text on Differential Calculus, or [3].
- 12.
Note, in order to convince oneself of the above statement, one needs first to write down the two \(2\times 2\) determinants on the right-hand side of (1.36); next to multiply them and write the result naturally as a \(2\times 2\) determinant. This resultant determinant consists of the four terms given as (1.37) and (1.38). It should be identical to the \(2\times 2\) determinant on the left-hand side of (1.36).
- 13.
References
A.B. Pippard, Elements of Classical Thermodynamics (Cambridge University Press, Cambridge, 1957), pp. 7–11
D. ter Haar, H. Wergeland, Elements of Thermodynamics (Addison-Wesley, Reading, 1966)
M.L. Boas, Mathematical Methods in the Physical Sciences, 3rd edn. (Wiley, New York, 2005)
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Tahir-Kheli, R. (2020). Definitions and the Zeroth Law. In: General and Statistical Thermodynamics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-20700-7_1
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