Embibe Experts Solutions for Chapter: Behaviour of Perfect Gas and Kinetic Theory, Exercise 1: Level 1

Consider a sample of oxygen behaving like an ideal gas. At $300 \mathrm{K}$, the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be :

(Molecular weight of oxygen is $32 \mathrm{g} {\mathrm{mol}}^{-1}; R=8.3 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$)

Assertion: An ideal gas is enclosed within a container fitted with a piston. When volume of this enclosed gas is increased at constant temperature, the pressure exerted by the gas on the piston decreases.

Reason: In the above situation, the rate of molecules striking the piston decreases. If the rate ạt which molecules of a gas having same average speed striking a given area of the wall decreases, the pressure exerted by gas on the wall decreases.

The volume $V$ of an enclosure contains a mixture of three gases, $16 \mathrm{g}$ of oxygen, $28 \mathrm{g}$ of nitrogen and $44 \mathrm{g}$ of carbon dioxide at absolute temperature $T$. Consider $R$ as universal gas constant. The pressure of the mixture of gases is :

One $\mathrm{kg}$ of a diatomic gas is at pressure of $8\times {10}^4 \mathrm{N} {\mathrm{m}}^{-2}$. The density of the gas is $4 \mathrm{kg} {\mathrm{m}}^{-3}$. What is the energy of the gas due to thermal motions?

A mixture of $2$ moles of helium gas (atomic mass$=4 \mathrm{amu}$) and $1$ mole of argon gas (atomic mass$=40 \mathrm{amu}$) is kept at $300 \mathrm{K}$ in a container. The ratio of the rms speed $\left(\frac{v_{\mathrm{rms}}\left(\mathrm{helium}\right)}{v_{\mathrm{rms}}\left(\mathrm{argon}\right)}\right)$ is

A gas mixture consists of $2$ moles of oxygen and $4$ moles of argon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is

Figure shows graphs of pressure vs density for an ideal gas at two temperatures $T_1$ and $T_2.$

In the following $V-T$ diagram what is the relation between $P_1$ and $P_2$