Question

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 $B$ 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 :

• A. $T_f=\frac{3}{7}{T}_0$
• B. $T_f=\frac{7}{3}{T}_0$
• C. $T_f=\frac{3}{2}{T}_0$
• D. $T_f=\frac{5}{2}{T}_0$

Answer 1

Answer: (C)

Here, change in internal energy of the system is •icro. i.e., increase in internal energy of one is equal to decrease in internal energy of other.
$\Delta U_A=1\times \frac{5R}{2}\left(T_f-T_0\right)$
$\Delta U_B=1\times \frac{3R}{2}\left(T_f-\frac{7}{3}{T}_0\right)$
Now $\Delta U_A+\Delta U_B=0$
$\frac{5R}{2}\left(T_f-T_0\right)+\frac{3R}{2}\left(T_f-\frac{7T_0}{3}\right)=0$
$5T_f-5T_0+3T_f-7T_0=0$
$\Rightarrow 8T_f=12T_0\Rightarrow T_f=\frac{12}{8}{T}_0=\frac{3}{2}{T}_0$