When $16 \ gm$ of $O_2$ at $37^{\circ}C$ is added to $22 \ gm$ of $CO_2$ at $27^{\circ}C$,what is the final temperature in $^{\circ}C$?

$A$ mixture of $2$ moles of oxygen and $4$ moles of argon is kept at temperature $T$. Neglecting all internal vibrations,the total internal energy of the system is: (in $, RT$)

Two rigid boxes placed on a table contain different ideal gases. Box $A$ contains $1 \text{ mole}$ of nitrogen at temperature $T_0$. Box $B$ contains $1 \text{ mole}$ of helium at temperature $(7/3) T_0$. Both boxes are brought into thermal contact,and heat flows until they reach a common final temperature $T_f$. (Neglect the heat capacity of the boxes). Express the final temperature $T_f$ in terms of $T_0$.

Two containers of equal volume contain identical gases at pressures $P_1$ and $P_2$ and absolute temperatures $T_1$ and $T_2$ respectively. The vessels are joined and the gas reaches a common pressure $P$ and a common temperature $T$. Then:

The molar heat capacity of a mixture of two gases at constant volume is $13R/6$. The ratio of the number of moles of the first gas to the second is $1:2$. The respective gases may be:

Four moles of hydrogen,two moles of helium and one mole of water vapour form an ideal gas mixture. $[C_v$ for hydrogen $= \frac{5}{2} R, C_v$ for helium $= \frac{3}{2} R, C_v$ for water vapour $= 3 R]$. What is the molar specific heat at constant pressure of the mixture?