Three perfect gases at absolute temperatures $T_1, T_2$ and $T_3$ are mixed. The masses of molecules are $m_1, m_2$ and $m_3$ and the number of molecules are $n_1, n_2$ and $n_3$ respectively. Assuming no loss of energy,the final temperature of the mixture is

Considering the gases to be ideal,the value of $\gamma = \frac{C_P}{C_V}$ for a gaseous mixture consisting of $3$ moles of carbon dioxide and $2$ moles of oxygen will be $(\gamma_{O_2} = 1.4, \gamma_{CO_2} = 1.3)$.

$A$ mixture of ideal gas containing $5$ moles of monatomic gas and $1$ mole of rigid diatomic gas is initially at pressure $P_0$,volume $V_0$ and temperature $T_0$. If the gas mixture is adiabatically compressed to a volume $V_0 / 4$,then the correct statement$(s)$ is/are:
(Given $2^{1.2}=2.3$; $2^{3.2}=9.2$; $R$ is gas constant)
$(1)$ The final pressure of the gas mixture after compression is in between $9 P_0$ and $10 P_0$.
$(2)$ The average kinetic energy of the gas mixture after compression is in between $18 RT_0$ and $19 RT_0$.
$(3)$ The work $|W|$ done during the process is $13 RT_0$.
$(4)$ Adiabatic constant of the gas mixture is $1.6$.

Three ideal gases at absolute temperatures $T_1, T_2,$ and $T_3$ are mixed. The number of molecules are $n_1, n_2,$ and $n_3$ respectively. Assuming no loss of energy,what is the final temperature of the mixture?

If $2 \text{ mole}$ of an ideal monoatomic gas at temperature $T$ is mixed with $6 \text{ mole}$ of another ideal monoatomic gas at temperature $2T$,then the temperature of the mixture is:

The specific heat of the mixture of two gases at constant volume is $\frac{13}{6} R$. The ratio of the number of moles of the first gas to the second is $1:2$. The respective gases may be: