Surface tension gases. The pressure inside an ideal (one surface) soap bubble can be derived from thermodynamic free energy considerations. At constant temperature and particle number, , the differential Helmholtz energy is given by where is the difference in pressure inside and outside of the bubble, and is the surface tension. In equilibrium, , and so, For a spherical bubble, the volume and surface area are given simply by and Substituting these relations into the previous expression, we find which is equivalent to the Young–Laplace equation when . For real soap bubbles, the pressure is doubled due to the presence of two
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