Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take the molar mass of helium $M_1 = 4 \ g/mol$ and that of hydrogen $M_2 = 2 \ g/mol$. The equivalent value of $\gamma$ for the mixture is:

If a gaseous mixture consists of $3$ moles of oxygen and $4$ moles of argon at an absolute temperature $T$,then the total internal energy of the mixture is (neglect vibrational modes and $R$ - Universal gas constant). (in $RT$)

Two identical containers contain the same gas at pressures $P_1$ and $P_2$ and temperatures $T_1$ and $T_2$,respectively. If the containers are connected,the common pressure is $P$ and the common temperature is $T$. What is the value of $P/T$?

$A$ mixture of $4$ moles of hydrogen,$1$ mole of helium,and $1$ mole of water vapor is treated as an ideal gas mixture. What is the molar specific heat of the mixture at constant pressure?

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:

$N_1$ molecules of a gas at temperature $T_1$ are mixed with $N_2$ molecules at temperature $T_2$. The resulting temperature of the mixture gas is