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Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_0$, while Box contains one mole of helium at temperature $(7/3)$ $T_0$ The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases,$T_f$ in terms of $T_0$ is
$T_f=$ $\frac{5}{2}\;$$T_0$
$T_f=$ $\frac{3}{7}\;$$T_0$
$T_f=$ $\;\frac{7}{3}\;$$T_0$
$T_f=$$\;\frac{3}{2}\;$$T_0$
Solution
$Heat\, lost \,by\, He=Heat\,gained\,by\,N_2$
${n_1}{C_{{v_1}}}\Delta {T_1} = {n_2}{C_{{v_2}}}\Delta {T_2}$
$\frac{3}{2}R\left[ {\frac{7}{3}{T_0} – {T_f}} \right] = \frac{5}{2}R\left[ {{T_f} – {T_0}} \right] \Rightarrow {T_f} = \frac{3}{2}{T_0}$
