A vessel contains $1$ mole of $O_2$ gas (molar mass $32$) at a temperature $T$. The pressure of the gas is $p$. An identical vessel containing one mole of He gas (molar mass $4$) at temperature $2\mathrm{T}$ has a pressure of

Pressure versus temperature graph of an ideal gas is as shown in figure. Density of the gas at point $A$ is ${\rho }_0$. Density at $B$ will be,

Two different isotherms representing the relationship between pressure $p$ and volume $V$ at a given temperature of the same ideal gas are shown for masses $m_1$ and $m_2$, then

Each atom of mass $m$ of a monoatomic gas has got three degrees of freedom. The $\mathrm{rms}$ velocity of these atoms is $v$ at temperature $T.$ For a diatomic molecule of mass $m$ and temperature $T$, which has got five degrees of freedom, rms velocity of molecule is,

The mass of hydrogen molecule is $3.32\times {10}^{-27} \mathrm{kg}$. If ${10}^{23}$ hydrogen molecules strike per second at $2 {\mathrm{cm}}^2$ area of a rigid wall at an angle of $45°$ from the normal and rebound back with a speed of $1000 \mathrm{m} {\mathrm{s}}^{-1}$, then the pressure exerted on the wall is,

A ring shaped tube contains two ideal gases with equal masses and relative molar masses $M_1=32$ and $M_2=28$. The gases are separated by one fixed partition $p$ and another movable stopper $S$, which can move freely without friction inside the ring.

The angle $\alpha$ in equilibrium as shown in the figure (in degrees) is