Solid angle is much, much farther away. The solid angle subtended by the complete ()-dimensional spherical surface of the unit sphere in -dimensional Euclidean space can be defined in any number of dimensions . One often needs this solid angle factor in calculations with spherical symmetry. It is given by the formula where is the gamma function. When is an integer, the gamma function can be computed explicitly. It follows that This gives the expected results of 4 steradians for the 3D sphere bounded by a surface of area and 2 radians for the 2D circle bounded by a circumference of length
Einstein solid Walther Nernst learned of Einstein's 1906 paper on specific heat, he was so excited that he traveled all the way from Berlin to Zürich to meet with him. The heat capacity of an object at constant volume "V" is defined through the internal energy "U" as formula_3, the temperature of the system, can be found from the entropy To find the entropy consider a solid made of formula_5 atoms, each of which has 3 degrees of freedom. So there are formula_6 quantum harmonic oscillators (hereafter SHOs for "Simple Harmonic Oscillators"). Possible energies of an SHO are given by or, in