This post details some aspects of the physical, chemical and mathematical behavior around high-altitude ballooning which after understood will allow us to derive important characteristics of gas balloons important to correctly dimension the system. We will focus on helium balloons but whenever applicable we shall explain the differences to hydrogen balloons.
In this post we shall introduce some important concepts that we will use in later posts.
Amount of substance
The amount of substance, also known as chemical amount, is a quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, and other particles. The SI unit for amount of substance is the mole, and its symbol is: mol.
Atomic weight
Let's first clarify that the weight of the elements has different names which are all synonymous: standard atomic weight (as it appears in the entry for each chemical element in Wikipedia, for example for helium), relative atomic mass and atomic weight (of the element) - read here, and here, the controversy around these names. Hereafter I will use mostly the name atomic weight because its is the name used by IUPAC, which is the institution responsible for publishing the atomic weights of the elements. The atomic weights are published by the IUPAC and revised each 2-years. Here we have their revision of 2009, and here their periodic table. Other source could be the Wikipedia periodic table with atomic weights, but from there it is not clear which revision of IUPAC they are using. Other source, from the Stanford university, presents not the atomic weights but the molecular weight (relative molar mass), using the deprecated IUPAC Recommended Atomic Weights of 1997. The molecular weight for elements like Helium is the same than the atomic weight because Helium has only 1 atom. But for elements like Atmospheric Nitrogen (N2) that is diatomic, the molecular weight is 2x the molecular weight (in this case = to atomic weight) of the monatomic N.
The atomic weight of element E is represented by the symbol: Ar(E).
The atomic weight is presented as a dimensionless physical quantity, and even in the existing tables no units are provided. See also the IUPAC article "ATOMIC WEIGHT -THE NAME, ITS HISTORY, DEFINITION, AND UNITS" where the dimensionless nature of th eatomic weight is referred. But then in every place where the atomic weight is used for some calculation, it is expressed as a quantity of grams per mole. For instance in this well explained course of Carnegie Mellon University. So for all the calculation hereafter, and until we get some better explanation of the above, we shall consider the atomic weight has being a quantity of grams per mole.
To give an an example, by consulting table 4 of the IUPAC Recommended Atomic Weights of 2009, where the atomic weights are abridged to four significant digits, and which apply to elements of natural terrestrial origin (as our balloon helium does), we can see that the Helium has an atomic weight of approximately 4.003, which as explained above, we will interpret as Helium weighting approximately 4.003 grams per mole.
Standard conditions for temperature and pressure
The Standard conditions for temperature and pressure, better known as STP, are "standard sets of conditions for experimental measurements established to allow comparisons to be made between different sets of data". Different institutions may follow different values for the STP, but we shall follow the values recommend by the IUPAC for chemistry:
- Temperature of 273.15 K (0 °C, 32 °F) and
- an absolute pressure of 100 kPa (14.504 psi, 0.986 atm, 1 bar)
Latter on well shall use the STP for making some calculations that depend on the temperature and pressure: as the temperature and pressure depend on the altitude, and as a balloon may be in different altitudes, sometimes is good to make a simplification and just consider the STP.
Gas constant
The gas constant (also known as ideal, universal or molar gas constant) is a "physical constant which is featured in many fundamental equations in the physical sciences, like bellow in the ideal gas law. It is denoted by the symbol R. Physically, the gas constant is the constant of proportionality that happens to relate the energy scale to the temperature scale, when a mole of particles at the stated temperature is being considered. The value for this constant is recommended by the Committee on Data for Science and Technology (CODATA) for international use. The value we shall use comes from the "CODATA Recommended Values of the Fundamental Physical Constants: 2010" which are in-line with the values presented in the gas constant entry in Wikipedia:
R= 8.3144621(75) J mol-1 K-1
The gas constant can be presented in a multitude of different units. In the gas constant entry in Wikipedia we can count the constant R as being available in 23 different units. We should choose the unit of the R constant in accordance to the unit(s) that we then want then the result of our calculations. In our case, and for the calculations that shall be presented in future posts, we shall use the R constant as:
R= 0.08205746(14) L atm K-1 mol-1
Ideal gas law
The ideal gas law "is the equation of state of a hypothetical ideal gas" - it approximates the behaviour of many gases under many circumstances. But be aware that is just an approximation - the reality shows that different gases behave differently. This equation relates pressure, volume and temperature to determine the state of a gas. We shall use this equation in its common form:
PV = nRT
where:
P = pressure of the gas;
V = volume of the gas;
n = amount of substance of gas (see above);
R = gas constant (see above);
T = temperature
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