Calculate y (ratio of C_p and C_V) for  triatomic linear gas at high temperature. Assume that the contribution of vibrational degree of freedom is 75% :

A vessel of uniform cross-section of length $500$ as shown figure is divided in two parts by a weightless & frictionless piston one part contains $5$ moles of ${\mathrm{N}}_2\left(\mathrm{g}\right)$ and other part contains $2$ moles of ${\mathrm{H}}_2\left(\mathrm{g}\right)\&1$ mole of $\mathrm{He}\left(\mathrm{g}\right)$ gaseous mixture at the same temperature and pressure.

What is the length of ${\mathrm{N}}_2$ compartment?

(Assume volume of piston to be negligible)

In two different vessels $\mathrm{A}$ and $\mathrm{B}$ containing ${\mathrm{H}}_2\mathrm{O}\left(\ell \right)$ at the same temperature, the vacant space left over the surface of ${\mathrm{H}}_2\mathrm{O}\left(\ell \right)$ is $\mathrm{V}$ and $4 \mathrm{V}$. What is the ratio of $\left[(\mathrm{K}·\mathrm{E}{)}_{\mathrm{A}}/(\mathrm{K}·\mathrm{E}{)}_{\mathrm{B}}\right]$ of vapour's in two vessels?

What is the mass of ${\mathrm{H}}_2\mathrm{O}$ present in air in $10$ litre closed vessel with $80\%$ relative humidity at $1 \mathrm{atm}$ and $300 \mathrm{K}$ ?

Given: Vapour pressure of ${\mathrm{H}}_2\mathrm{O}$ is $30$ torr at $300 \mathrm{K}$.