(20 points) Consider two paramagnets, 1 and 2, which are initially thermally isolated from each other and whose total multiplicity is represented by 1(q1,N1)2(qq1,N2) where paramagnets is removed and the two systems are allowed to come to thermal equilibrium. Answer the following questions: a. Determine the change in the entropy of the total system when the two paramagnets reach a thermal equilibrium. b. At thermal equilibrium determine the energy unit q0 associated with paramagnet 1 which gives the highest multiplicity component 1(q0,N1)2(qq0,N2) in the sum (q,N)=x=0q1(x,N1)2(qx,N2) where q=q1+q2,N=N1+N2. This gives the total multiplicity of the combined system at thermal equilibrium. c. (10 points) This part shows the sharpness of the 1(x,N1)2(qx,N2) function. Assume that x=q0+ where