$A$ mixture of carbon dioxide and oxygen has volume $8310 \text{ cm}^3$, temperature $300 \text{ K}$, pressure $100 \text{ kPa}$ and mass $13.2 \text{ g}$. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are . . . . . . . (Assume both carbon dioxide and oxygen gases behave like ideal gases) $[R = 8.31 \text{ J/mol.K}]$

$A$ cylinder consists of a gas mixture of helium and oxygen. If the mass of helium is $4 \,g$ and the mass of oxygen is $32 \,g$, then the ratio of specific heat of the mixture $\left(C_p / C_V\right)$ is:

$A$ mixture of ideal gases has $2$ moles of $He$,$4$ moles of oxygen $(O_2)$,and $1$ mole of ozone $(O_3)$ at absolute temperature $T$. The internal energy of the mixture is ............. $RT$.

The pressure and temperature of two different gases are $P$ and $T$,each having the same volume $V$. If they are mixed while keeping the volume and temperature constant,the pressure of the mixture will be:

Two ideal gases $A$ and $B$ having the same temperature $T$,same pressure $P$,and same volume $V$,are mixed together. If the temperature of the mixture is kept constant and the volume occupied by the mixture is reduced to $\frac{V}{2}$,then the pressure of the mixture will become:

$A$ 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 $1.6$.