Problem S2.4. An insulated box with fixed total volume V is partitioned into m insulated compartments, each containing an ideal gas of a different molecular species. Assume that each compartment has the same pressure but a different number of moles, a different temperature, and a different volume. (The thermodynamic variables for the ith compartment are (P, ni, Ti, Vi).) If all partitions are suddenly removed and the system is allowed to reach equilibrium:

(a) Find the final temperature and pressure, and the entropy of mixing. (Assume that the particles are monatomic.)

(b) For the special case of m= 2 and parameters n = 1 mol, T = 300 K, V = 1 liter, n = 3 mol, and V = 2 liters, obtain numerical values for all parameters in part (a). =

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V, P, T Nia, N16 V, P, T N2a, N26 2V, P, T Na Na Na == N = N1b + N2b