Question

Consider two boxes of ideal gas. The boxes are thermally isolated from the world, and initially from each other as well. Each box holds N molecules in volume V. Box #1 starts with temperature T_i,1 while #2 starts with T_i,2. (The subscript “i” means “initial,” and “f” will mean “final.”) So, the initial total energies are E_i,1 = (3/2)Nk_BT_i,1 and E_i,2 = (3/2)Nk_BT_i,2.

Now we put the boxes into thermal contact with each other, but still isolated from the rest of the world. Eventually we know they’ll come to the same temperature, as argued in Equation 6.10: T_A=T_B.

a. What is this temperature? *(Hint: # of molecules in combined box is 2N)

b. Show that the change of total entropy Stot =

(Hint: You can use the simple version of Sakur-Tetrode derived as your starting point. You can also use E = (3/2)k_BT

S = - Sakur-Tetrode equation

c. Show that this change is always ≥ 0. [Hint: Let X = and express the change of entropy in terms of X. Plot the resulting function of X.]

d. Under a special circumstance the change in S_tot will be zero: When? Why?

*This is Molecular Biophysics level. Please be as specific (easy to understand) as possible. I need help.

Answer 1