The fraction of molecular volume to the actual volume occupied by oxygen gas at STP is: (Take the diameter of an oxygen molecule to be 3 Å).
1. 4 × 10⁻⁴
2. 5 × 10⁻⁴
3. 3 × 10⁻⁴
4. 1 × 10⁻⁴

The figure shows a plot of $\dfrac{PV}{T}$ versus $P$ for $1.00\times10^{-3}$ kg of oxygen gas at two different temperatures.

Then relation between $T_1$ and $T_2$ is: 
1. $T_1=T_2$
2. $T_1<T_2$
3. $T_1>T_2$
4. $T_1 \geq T_2$

            
The value of $\frac{PV}{T}$ where the curves meet on the $y\text-$axis is:
1. $0.06~\text{JK}^{-1}$
2. $0.36~\text{JK}^{-1}$
3. $0.16~\text{JK}^{-1}$
4. $0.26~\text{JK}^{-1}$

An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm, and its temperature drops to 17 °C. The mass of oxygen taken out of the cylinder is: $\left(\mathrm{R}=8.31 {\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}, \mathrm{molecular} \mathrm{mass} \mathrm{of} {\mathrm{O}}_2=32 \mathrm{u}\right)$

1. 0.14 kg
2. 0.16 kg
3. 0.18 kg
4. 0.21 kg

An air bubble of volume 1.0 $c{m}^3$ rises from the bottom of a lake 40 m deep at a temperature of 12 °C. To what volume does it grow when it reaches the surface, which is at a temperature of 35 °C?
1. 5.3 cm³
2. 4.0 cm³
3. 3.7 cm³
4. 4.9 cm³

What is the total number of air molecules (inclusive of oxygen, nitrogen, water vapor, and other constituents) in a room of capacity $25.0$ m³ at a temperature of $27^\circ \text C$ and $1$ atm pressure?
1. $6.1\times10^{23}$ molecules
2. $6.1\times10^{26}$ molecules
3. $7.1\times10^{23}$ molecules
4. $7.1\times10^{26}$ molecules

At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the RMS speed of a helium gas atom at $-20^\circ \text{C}?$
(Given the atomic mass of $\mathrm{Ar}=39.9~\text{u}$ and of $\mathrm{He}=4.0~\text{u}$)
1. $1.01 \times 10^3 ~\text{K}$
2. $3.15 \times 10^3 ~\text{K}$
3. $1.91 \times 10^3~ \text{K}$
4. $2.52 \times 10^3 ~\text{K}$

From a certain apparatus, the diffusion rate of hydrogen has an average value of $28.7~\text{cm}^3 \text{s}^{-1}.$ The diffusion of another gas under the same conditions is measured to have an average rate of $7.2~\text{cm}^3 \text{s}^{-1}.$ The unknown gas is:
1. Oxygen
2. Nitrogen
3. Helium
4. None of these