The average thermal energy for a mono-atomic gas is:
(\(k_B\) is Boltzmann constant and \(T\) absolute temperature)

1.	\(\dfrac{3}{2}k_BT\)	2.	\(\dfrac{5}{2}k_BT\)
3.	\(\dfrac{7}{2}k_BT\)	4.	\(\dfrac{1}{2}k_BT\)

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

A cylinder contains hydrogen gas at a pressure of \(249~\text{kPa}\) and temperature \(27^\circ\text{C}.\) 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 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

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. \(T_1 \geq T_2\)$\mathrm{}$

The value of \(\frac{PV}{T}\) where the curves meet on the \(y\)-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cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm, and its temperature drops to 17 °C. The mass of oxygen taken out of the cylinder is: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