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(C) The total internal energy of the mixture is the sum of the internal energies of the individual gases.For a gas,the internal energy is given by $U

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$\frac{(N_1 T_1 + N_2 T_2)}{(N_1 + N_2)}$

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(C) The total internal energy of the mixture is the sum of the internal energies of the individual gases.For a gas,the internal energy is given by $U = \frac{3}{2} N k T$.Total internal energy $U_{total} = U_1 + U_2 = \frac{3}{2} N_1 k T_1 + \frac{3}{2} N_2 k T_2$.Let the final temperature of the mixture be $T$. The total internal energy of the mixture is $U_{final} = \frac{3}{2} (N_1 + N_2) k T$.By the law of conservation of energy,$U_{total} = U_{final}$.$\frac{3}{2} N_1 k T_1 + \frac{3}{2} N_2 k T_2 = \frac{3}{2} (N_1 + N_2) k T$.Canceling the common factor $\frac{3}{2} k$ from both sides:$N_1 T_1 + N_2 T_2 = (N_1 + N_2) T$.Therefore,the resulting temperature is $T = \frac{N_1 T_1 + N_2 T_2}{N_1 + N_2}$.

$N_1$ molecules of a gas at temperature $T_1$ are mixed with $N_2$ molecules at temperature $T_2$. The resulting temperature of the mixture gas is

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