The molecular picture of a perfect (ideal) gas will just be stated here. In the later performed statistical approach this microscopic picture will directly allow to calculate the macroscopic equations.
Continuous and random distribution of atoms/molecules (rigid spheres)
Speed of particles increases with temperature, internal energy of perfect gas depends on temperature ONLY
No interaction of particles except elastic collisions, i.e. NO attractive or repulsive forces between particles
The molecules are widely separated and move in paths that are largely unaffected by intermolecular forces.
The macroscopic picture of a perfect gas follows a general scheme applicable to all systems.
Defined by an equation of state, e.g. \(p = F(T,V,n)\), mostly containing three independent variables (i.e. knowledge of three variables fixes the fourth one)
Extensive variables: depend on the extent of the system, e.g.
Volume \(V\), mass \(m\), internal energy \(U\)
However, for comparison of distinct compounds: molar or specific quantities
Intensive variables: independent of the extent of the system, e.g.
Temperature \(T\), pressure \(p\), density \(\rho\)
Intensive variables of ideal mixtures: number average of a quantity \(\Gamma\)
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| \begin{equation*} \Gamma = \frac{\sum_i N_i \Gamma_i }{\sum_i N_i} \label{intensiv_par_mixing} \end{equation*} | (1.1) |
where \(\Gamma_i\) is the intensive property of particle type \(i\) and \(N_i\) the corresponding particle number. An example for an ideal mixture average value is temperature. Mixing \(N_a\) particles at \(T_a\) with \(N_b\) particles at \(T_b\) results in a weighted mean value
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| \begin{equation*} T = \frac{N_a \;T_a + N_b \;T_b}{N_a + N_b} \end{equation*} | (1.2) |
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© J. Carstensen (TD Kin I)