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Decimal expansion of 3/8.
0

%I #36 Feb 15 2023 10:06:44

%S 3,7,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Decimal expansion of 3/8.

%C This is the value of Zc which is the critical compression factor for Van der Waals gases.

%C The compression factor of a gas is defined as Z = p Vm/RT, where p is the pressure, Vm is the molar volume, T the temperature and R the gas constant.

%C The critical forms for Van der Waals gasses of pressure, temperature and volume are respectively: pc = a/(27b^2), Tc = 8a/(27R*b), Vc = 3b.

%C By plugging in the critical forms of the variables you will get Zc = pc Vc/RTc = 3/8.

%C Probability of intersection of 2 random chords in a circle, when their midpoints are selected randomly in the circle. See Solomon. - _Michel Marcus_, Mar 29 2018

%C The distance of the centroid of a unit-radius solid hemisphere from its base (the 3D analog of A232715). - _Amiram Eldar_, Jul 19 2022

%C The binomial transform is 3, 10, 22, 39,... A140066 without the leading 1. - _R. J. Mathar_, Feb 15 2023

%D Peter Atkins, Julio de Paula, Physical Chemistry 8th Ed., W. H. Freeman and Company, 2006, pp. 14-21.

%H Herbert Solomon, <a href="https://archive.org/stream/GeometricProbability/Geometric_Probability-Solomon#page/n161/mode/2up">Geometric Probability</a>, SIAM, 1978, p. 152.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Compressibility_factor">Compressibility factor</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Van_der_Waals_equation">Van der Waals equation</a>.

%e 0.3750000...

%t First@ RealDigits[N[3/8, 105]] (* _Michael De Vlieger_, May 15 2018 *)

%o (PARI) my(x=3/8); for(k=1, 100, my(d=floor(x)); x=(x-d)*10; k>1 && print1(d, ", ")) \\ _Felix Fröhlich_, Mar 28 2018

%Y Cf. A232715.

%K nonn,easy,cons

%O 0,1

%A _Natan Arie Consigli_, Mar 26 2018