$A$ gas mixture contains monoatomic and diatomic molecules of $2$ moles each. The mixture has a total internal energy of (symbols have usual meanings): (in $R T$)

One litre of oxygen at a pressure of $1 \,atm$ and two litres of nitrogen at a pressure of $0.5 \,atm$ are introduced into a vessel of volume $1 \,L$. If there is no change in temperature,the final pressure of the mixture of gas (in $atm$) 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 $(\gamma_{O_2} = 1.4, \gamma_{CO_2} = 1.3)$.

The relation between internal energy $U$,pressure $P$,and volume $V$ for an ideal gas is given by $U = 2 + 2PV$. The gas is:

The ratio $C_P / C_V$ for a gas mixture consisting of $8 \ g$ of helium and $16 \ g$ of oxygen is

Consider a mixture of $n$ moles of helium gas and $2n$ moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its $\frac{C_{P}}{C_{V}}$ value will be