$A$ gas mixture consists of $2$ moles of oxygen and $4$ moles of neon at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system will be $...........\,RT$.

$14 \, g$ of $CO$ at $27^{\circ} C$ is mixed with $16 \, g$ of $O_2$ at $47^{\circ} C$. The temperature of the mixture is .......... $^{\circ} C$ (vibration mode neglected).

$3$ moles of mono-atomic gas $(\gamma = 5/3)$ is mixed with $1$ mole of a diatomic gas $(\gamma = 7/5)$. The value of $\gamma$ for the mixture will be

If $4$ moles of an ideal monoatomic gas at temperature $400 \,K$ is mixed with $2$ moles of another ideal monoatomic gas at temperature $700 \,K$, the temperature of the mixture is:

$A$ vessel contains two non-reactive gases: neon (monatomic) and oxygen (diatomic). The ratio of their partial pressures is $3:2$. Estimate the ratio of
$(i)$ number of molecules and
$(ii)$ mass density of neon and oxygen in the vessel.
Atomic mass of $Ne = 20.2 \; u$,molecular mass of $O_2 = 32.0 \; u$.

$A$ 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 $1.6$.