Two moles of helium are mixed with $n$ moles of hydrogen. If $\frac{C_P}{C_V} = \frac{3}{2}$ for the mixture,then the value of $n$ is:

Two monoatomic ideal gases at temperatures $T_1$ and $T_2$ are mixed. There is no loss of energy. If the masses of molecules of the two gases are $m_1$ and $m_2$ and the number of their molecules are $n_1$ and $n_2$ respectively,the temperature of the mixture will be:

$A$ rigid tank contains $35 \, kg$ of nitrogen at $6 \, atm$. $A$ sufficient quantity of oxygen is supplied to increase the pressure to $9 \, atm$,while the temperature remains constant. The amount of oxygen supplied to the tank is .... $kg$.

Two ideal gases at absolute temperatures $T_1$ and $T_2$ are mixed. There is no loss of energy. The masses of the molecules are $m_1$ and $m_2$ and the number of molecules in the gases are $n_1$ and $n_2$ respectively. The temperature of the mixture will be:

$3\, \text{moles}$ 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.

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