If $\alpha$ moles of a monoatomic gas are mixed with $\beta$ moles of a polyatomic gas and the mixture behaves like a diatomic gas,then [neglect the vibrational mode of freedom]:

$A$ mixture of two non-reactive ideal gases is enclosed in a vessel consisting of one mole of a monatomic gas '$A$' and 'n' moles of a diatomic gas '$B$' at a temperature '$T$'. If the adiabatic constant of the gaseous mixture is $\frac{13}{9}$,then the value of 'n' is:

One gram of $H_2$ at $27\,^{\circ}C$ is mixed with $16\,g$ of $O_2$ at $37\,^{\circ}C$. The temperature of the mixture is about ....... $^{\circ}C$.

$A$ gas mixture consists of $2.0$ moles of oxygen and $4.0$ moles of neon at temperature $T$. Neglecting all vibrational modes, calculate the total internal energy of the system. (Oxygen has two rotational modes.) (in $RT$)

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 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