The Hamiltonian for a free classical ideal gas of N atoms can be written as H=p}+p%+…+px, where we have chosen units such that 2m = 1. (a) Show that the phase-space volunie is r(E, V) = K, VNEa(vĒ), where Ko is aconstant, and n= 3N. (b) Calcuļate Eg, and obtain the entropy S(E, V). Verify that it agrees with the result from thermodynanics.

The Hamiltonian for a free classical ideal gas of N atoms can be written as H=p}+p%+…+px, where we have chosen units such that 2m = 1. (a) Show that the phase-space volunie is r(E, V) = K, VNEa(vĒ), where Ko is aconstant, and n= 3N. (b) Calcuļate Eg, and obtain the entropy S(E, V). Verify that it agrees with the result from thermodynanics.