$A$ gas mixture contains $n_1$ moles of a monoatomic gas and $n_2$ moles of a gas of rigid diatomic molecules. Each molecule in the monoatomic and diatomic gas has $3$ and $5$ degrees of freedom respectively. If the adiabatic exponent $\left(\frac{C_p}{C_V}\right)$ for this gas mixture is $1.5$, then the ratio $\frac{n_1}{n_2}$ will be

Two different gases have pressure $P$ and temperature $T$. Their volume is $V$. If these two gases are mixed while keeping the volume and temperature the same,the pressure of the mixture will be...........

One mole of a gas with $\gamma = 7/5$ is mixed with one mole of a gas with $\gamma = 4/3$. What will be the $\gamma$ of the mixture?

If a gaseous mixture consists of $3$ moles of oxygen and $4$ moles of argon at an absolute temperature $T$,then the total internal energy of the mixture is (neglect vibrational modes and $R$ - Universal gas constant). (in $RT$)

$A$ 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 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