G L Mittal and TARUN MITTAL Solutions for Chapter: Kinetic Theory of Gases, Exercise 2: NUMERICALS

A flask of the volume $1\times {10}^{-3} m^3$ contain $3.0\times {10}^{12}$ oxygen molecules at a certain temperature. The mass of one molecule of oxygen is $5.3\times {10}^{-26} kg$ and the root-mean-square velocity of its molecules at the same temperature is $400 m{s}^{-1}$. Calculate the pressure of the oxygen gas in the flask.

The density of a gas at normal pressure and $0°C$ temperature is $1.2 kg{m}^{-3}$. Calculate the root- mean-square velocity of the molecules of the gas at $0°C$.

The density of a gas at normal pressure and $0°C$ temperature is $1.2 kg{m}^{-3}$. Calculate the temperature at which the velocity will become three times the initial velocity.

The root-mean-square velocity of helium atoms at normal temperature and pressure is $1300 m{s}^{-1}$. Calculate density of helium at $0°C$.

The root-mean-square velocity of helium atoms at normal temperature and pressure is $1300 {\mathrm{ms}}^{-1}$. Calculate the mass of the helium atom.

The root-mean-square speed of oxygen molecules at a certain temperature is $150 m{s}^{-1}$. Calculate the root-mean-square speed of hydrogen molecules at the same temperature. Molecular weights of oxygen and hydrogen are respectively $32$ and $2$.

What will be the ratio of the root-mean-square speeds of the molecules of an ideal gas at $270 \mathrm{K}$ and $30 \mathrm{K}$?

At what temperature will the root-mean-square velocity of molecules of a gas be twice the root- mean-square velocity at $0°C$? At what temperature $1.5$ times?