consider a classical ideal gas in thermal equilibrium at temperature t in a container of volume v in the presence of a uniform gravitational field. the acceleration due to gravity is g and directed along the -z direction. (a) calculate the chemical potential j.i. of an element of volume of such a gas as a function of the pressure p, the temperature t, and the height z. (b) show that the requirement that j.i. is constant implies immediately the law of atmospheres which gives the dependence of p on t and z