Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
![1) State the number of degrees of freedom of a gas composed of one of the following
Ne (neon atom)
b. N2 (nitrogen molecule)
a.
2) A diatomic molecule which consists of two atoms can have translational, rotational, and vibrational
degrees of freedom because the molecule can translate, rotate, and vibrate. However, it is known
that just because a molecule is capable of rotating or vibrating does not mean that there is enough
energy available to do so. The temperature has to be high enough to enable different types of
motion. In that case, we say that the degree of freedom is active if the temperature is high enough
or inactive if it is not. How many degrees of freedom are active in a hydrogen molecule, H2, at 500
K?
3) Write an expression for the internal energy U of a gas of N particles (that is, atoms or molecules) at
temperature T in terms of N and T and any required constants, when the gas consists of
a. Ne (neon atoms)
b. N2 (nitrogen molecules), assuming all degrees of freedom are active.
4) Calculate the internal energy U of a liter of helium at room temperature and atmospheric pressure.
Then repeat the calculation for a liter of air.
5) The equipartition theorem allows us to write U = aNkT, where the constant a is the number of
(active) degrees of freedom per molecule and k is Boltzmann's constant. Write an expression for
the change in internal energy AU.
6) What does the expression for AU from the previous problem say about AU if the temperature is
constant?
a
22
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