Hydrogen is a diatomic gas. Its molar specific heat at constant volume is very nearly

$T _1$ is the temperature of oxygen enclosed in a cylinder. The temperature is increased to $T _2$ and Maxwellan distribution curves for $O _2$ at temperature $T _1$ and $T _2$ are plotted. If $A _1$ and $A _2$ are the areas under the curves and the speed axis, in both cases , then 

let A and B the two gases and given :
$\frac{{T} _{A}}{{M} _{A}}$ = 4. $\frac{{T} _{B}}{{M} _{B}}$  Where T is the temperature and M is molecular mass. If ${C} _{A}$ and  ${C} _{B}$ are the r.m.s. speed, then the ratio $\frac{{C} _{A}}{{C} _{B}}$ will be equal to:

A mixture of ideal gases 7 kg of nitrogen and 11 Kg of $ CO _2 $ then (Take $\gamma$ for nitrogen and $CO _2$ as 1.4 and 1.3 respectively)

$3$ mole of gas ''X"  and $2$ moles of gas "Y" enters from end "P" and "Q" of the cylinder respectively. The cylinder has the area of cross section , shown as
under 
The length of the cylinder is $150cm$. The gas "X" intermixes with gas "Y" at the point . If the molecular weight of the gases X and Y is $20$ and $80$ respectively, then what will be the distance of point A from Q?

The lowest pressure(the best Vaccum) that can be created in laboratory at 27 degree is $10^{-11} $ mm of Hg. At this pressure, the number of ideal gass molecules per $cm^{3}$ will be

If $P=10^6kT$, then the number of molecules per unit volume of the gas is:

A sample of gas is at $0^{\circ}C$. To what temperature must it be raised in order to double the rms speed of its molecules?

One mole of gas occupies 10 ml at 50 mm pressure. The volume of 3 moles of the gas at 100 mm pressure and same temperature is 

2 moles of an ideal monoatomic gas at temperature $T _0$ is mixed wth 4 moles of another ideal monoatomic gas at temperature $2T _0$ then  the temperature of the mixture is:

In two vessels of the same volume, atomic hydrogen and helium with pressure 1 atm and 2 atm are filled. If temperature of both the same is the same, then the average speed of hydrogen atom $v _H$ will be related to helium $v _{He}$ as

The molecular weights of $O _2$ and $N _2$ are 32 and 28 respectively. At $15^0$C, the pressure of 1 gm will be the same as that of 1 gm in the same bottle at the temperature.

Average kinetic energy of a gas molecule is

Maxwell's laws of distribution of velocities shows that

The average velocity of the molecules in a gas in equilibrium is

The average kinetic energy of a gas molecule at ${27}^{o}C$ is $6.21\times {10}^{-21}J$, then its average kinetic energy at ${227}^{o}C$ is:

For a given gas, which of the following relationships is correct at a given temp?

A vessel contains a mixture consisting of m$ _{1}$ - 7 g of nitrogen (M$ _{1}$ = 28) and m$ _{2}$ = 11 g of carbon dioxide (M$ _{2}$ = 44) at temperature T - 300 K and pressure P$ _{0}$ = 1 atm. The density of the mixture is

A vessel of volume V contains a mixture of $1$mole of hydrogen and $1$ mole of oxygen(both considered as ideal). Let $f _1(v)dv$ denote the fraction of molecules with speed between v and $(v+dv)$ with $f _2(v)dv$, similarly for oxygen. then