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

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

$A$ 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 $...........\,RT$.

$A$ gas mixture consists of molecules of type $1, 2$ and $3$,with molar masses $m_1 > m_2 > m_3$. $v_{rms}$ and $\bar K$ are the $r.m.s.$ speed and average kinetic energy of the gases. Which of the following is true?

One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas. The molar specific heat of the mixture at constant volume is