Question

A system is composed of two harmonic oscillators, each of natural frequency w, and having permissible energies "*1/2)w, where" is any non-negative integer. The total energy of the system is = 'hwo, where" is a positive integer. • For a given energy, how many microstates are available to the system? What is the entropy of the system? • A second system is also composed of two harmonic oscillators, each of natural frequency 2w,. The total energy of this system is " = "hwo , where "" is an even integer. • How many microstate are available to this system ? o What is the entropy of a system composed of the two preceeding subsystems (separated and enclosed by a totally restrictive wall)? Express the entropy as a function of F' and ".

Answer 1

I consider the above given that it composed of I hooronic oscillators energy of 1st hormonic oscillator En =(n+1) hab energy of and hormonic oscillator E=(+1) hwo total energy E = Ent Er =m+12) hwo t h + ) huo E = hwo (n+r+1) consider E = n'hwo : nantut litis posible in n'ways no. of microstates n'- E hwo energy Siakin E simillarly En = (nt) ħ awo

Em = (M+ - 1) tawo E" = (n+M+1) ħ wo sincillarly taken n"=nort) then E" = 2n"ħwo above condition number of possible resulty ntretin entropy = S2 = kilpola = Kiln 9h Wo total entropy of the system Sy = S, 7 S₂ = kin E + kly hwo Lk . . . . . . . example: = Incab) let x+y=5 Possibilites (x, y) = 10,5) (2, 4) -- 15,0 Total Posibulities = 5

let 2(x+y) = 2(5+8= 20