Apologize if you feel this question to be so simple and naive. Suppose a chamber is divided by a insulator into two equal volume (V) chambers, . One chamber contains n moles of hot oxygen at temperature T1, the other chamber contains n moles of cold oxygen at temperature T2. If you move the insulator away and let the hot & cold oxygen molecules to mix well. How much energy is lost during this process? I guess if you know how to compute the enthalpy/free energy/entropy of gas with volume V & amount in moles & temperature, then the answer is simply delta(E) = enthalpy(2n, (T1 + T2)/2, 2V) - enthalpy(n, T1, V) - enthalpy(n, T2, V)? One can replace enthalpy(n, t, v) with free_energy(n, t, v)? Thanks in advance.