Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take molar mass of helium $M_1=4\ g$ and that of hydrogen $M_2=2\ g$. If the internal energy of the $He$ sample is $100\ J$ and that of the hydrogen sample is $200\ J$,then the internal energy of the mixture is ..... $J$.

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:

$A$ 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:

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:

$A$ vessel of volume $0.02 \, m^3$ contains a mixture of hydrogen and helium at $20 \, ^oC$ and $2$ atmospheric pressure. The mass of the mixture is $5 \, g$. Find the ratio of the mass of hydrogen to that of helium in the mixture.

Four moles of hydrogen,two moles of helium,and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of the mixture?