$3\, \text{moles}$ of an ideal gas at a temperature of $27^{\circ}\, \text{C}$ are mixed with $2\, \text{moles}$ of an ideal gas at a temperature of $227^{\circ}\, \text{C}$. Determine the equilibrium temperature $(^{\circ}\, \text{C})$ of the mixture, assuming no loss of energy.

If a mixture of $28 \, g$ of Nitrogen $(N_2)$,$4 \, g$ of Hydrogen $(H_2)$,and $8 \, g$ of Helium $(He)$ is contained in a vessel at temperature $400 \, K$ and pressure $8.3 \times 10^5 \, Pa$,the density of the mixture will be:

$A$ mixture of gases consists of $16 \ g$ of Helium and $16 \ g$ of Oxygen. The ratio of specific heats of the mixture is nearly

$A$ closed container of volume $0.02 \ m^3$ contains a mixture of neon and argon gases at a temperature of $27^{\circ}C$ and a pressure of $1 \times 10^5 \ N/m^2$. The total mass of the mixture is $28 \ g$. If the atomic weights of neon and argon are $20$ and $40$ respectively,find the mass of each gas in the container in $g$,assuming they behave as ideal gases. $(R = 8.314 \ J/mol \cdot K)$

Two gases $A$ and $B$ having same pressure $P$,volume $V$,and absolute temperature $T$ are mixed. If the mixture has the volume and temperature as $V$ and $T$ respectively,then the pressure of the mixture is

One mole of monatomic gas and three moles of diatomic gas are put together in a container. The molar specific heat (in $J K^{-1} mol^{-1}$) at constant volume is (Let $R=8 \, J K^{-1} mol^{-1}$).