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:

$A$ gas mixture consists of $16 \ g$ of helium and $16 \ g$ of oxygen. For this mixture,the ratio $C_P/C_V$ is equal to:

Two ideal polyatomic gases at temperatures $T_{1}$ and $T_{2}$ are mixed such that there is no loss of energy. If $F_{1}$ and $F_{2}$,$m_{1}$ and $m_{2}$,$n_{1}$ and $n_{2}$ are the degrees of freedom,masses,and number of molecules of the first and second gas respectively,then the temperature of the mixture of these two gases is:

In a cubic container of inner side length $10 \ cm$, nitrogen gas at $100 \ kPa$ pressure is maintained at $300 \ K$. If the pressure inside the container is increased to $300 \ kPa$ by adding oxygen gas, the ratio of the number of $N_2$ molecules to $O_2$ molecules in the container is:

Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases which obey the Maxwellian distribution of velocities. Vessel $A$ contains only $O_2$,$B$ only $N_2$ and $C$ a mixture of equal quantities of $O_2$ and $N_2$. If the average speed of the $O_2$ molecules in vessel $A$ is $V_1$,and that of the $N_2$ molecules in vessel $B$ is $V_2$,what is the average speed of the $O_2$ molecules in vessel $C$?

$A$ 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 .... $kg$.