A301755 Decimal expansion of 3/8.

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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Natan Arie Consigli, Mar 26 2018

Keywords

• nonn
• easy
• cons

Comments

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

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.

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.

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

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

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

The binomial transform is 3, 10, 22, 39,... A140066 without the leading 1. - R. J. Mathar, Feb 15 2023

Examples

			0.3750000...
		

References

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

Links

• Herbert Solomon, Geometric Probability, SIAM, 1978, p. 152.
• Wikipedia, Compressibility factor.
• Wikipedia, Van der Waals equation.

Crossrefs

Cf. A232715.

Programs

Mathematica

First@ RealDigits[N[3/8, 105]] (* Michael De Vlieger, May 15 2018 *)

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