The mean free path of molecules of a gas (radius \(r\)) is inversely proportional to:
1. \(r^3\)
2. \(r^2\) 
3. \(r\) 
4. \(\sqrt{r}\)

The amount of heat energy required to raise the temperature of \(1\) g of Helium at NTP, from \({T_1}\) K to \({T_2}\) K is:
1. \(\frac{3}{2}N_ak_B(T_2-T_1)\)
2. \(\frac{3}{4}N_ak_B(T_2-T_1)\)
3. \(\frac{3}{4}N_ak_B\frac{T_2}{T_1}\)
4. \(\frac{3}{8}N_ak_B(T_2-T_1)\)

A gas mixture consists of \(2\) moles of \(\mathrm{O_2}\) and \(4\) moles of \(\mathrm{Ar}\) at temperature \(T.\) Neglecting all the vibrational modes, the total internal energy of the system is:

For hydrogen gas, the difference between molar specific heats is given by; \(C_P-C_V=a,\) and for oxygen gas, \(C_P-C_V=b.\) Here, \(C_P\)​ and \(C_V\)​ are molar specific heats expressed in \(\text{J mol}^{-1}\text{K}^{-1}.\) What is the relationship between \(a\) and \(b?\)
1. \(a=16b\)
2. \(b=16a\)
3. \(a=4b\)
4. \(a=b\)

The value \(\gamma = \frac{C_P}{C_V}\) for hydrogen, helium, and another ideal diatomic gas \(X\) (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to:

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

2. \( \dfrac{1}{\sqrt{2} n^2 \pi {d}^2} \)

3. \(\dfrac{1}{\sqrt{2} n^2 \pi^2 d^2} \)

4. \( \dfrac{1}{\sqrt{2} n \pi {d}}\)

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. \(0.5~\text{kg/m}^{3}\)

Which of the following diagrams (figure) depicts ideal gas behaviour?