A cylinder contains hydrogen gas at a pressure of \(249~\text{kPa}\) and temperature \(27^\circ~\mathrm{C}.\) Its density is: (\(R=8.3~\text{J mol}^{-1} \text {K}^{-1}\))
1. \(0.2~\text{kg/m}^{3}\)
2. \(0.1~\text{kg/m}^{3}\)
3. \(0.02~\text{kg/m}^{3}\)
4. \(0.5~\text{kg/m}^{3}\)

The average thermal energy for a mono-atomic gas is:
(\(k_B\) is Boltzmann constant and T absolute temperature)
1. \(\frac{3}{2}k_BT\)
2. \(\frac{5}{2}k_BT\)
3. \(\frac{7}{2}k_BT\)
4. \(\frac{1}{2}k_BT\)

An ideal gas equation can be written as $\mathrm{P}=\frac{\mathrm{\rho RT}}{{\mathrm{M}}_0}$ where $\mathrm{\rho }$ and ${\mathrm{M}}_0$ are respectively,

(1) mass density, the mass of the gas

(2) number density, molar mass

(3) mass density, molar mass

(4) number density, the mass of the gas

The mean free path for a gas, with molecular diameter \(d\) and number density \(n,\) can be expressed as:
1. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}^2} \)
2. \( \frac{1}{\sqrt{2} n^2 \pi \mathrm{d}^2} \)
3. \(\frac{1}{\sqrt{2} n^2 \pi^2 d^2} \)
4. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}}\)

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

Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure is:
(STP: \(1\) atmospheric pressure, \(0~^\circ \text{C}\))
1. \(0\) 
2. \(22.4\) litres
3. \(11.2\) litres
4. \(1\) litres

The figure shows a plot of \(\frac{PV}{T}\) 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. \(T_1 \geq T_2\)$\mathrm{}$

The figure shows a plot of PV/T versus P for $1.00\times {10}^{-3} kg$ of oxygen gas at two different temperatures.

The value of PV/T where the curves meet on the y-axis is:

$1. 0.06 J K^{-1}$
$2. 0.36 J K^{-1}$
$3. 0.16 J K^{-1}$
$4. 0.26 J K^{-1}$

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cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm, and its temperature drops to 17 °C. The mass of oxygen taken out of the cylinder is: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