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:
1. \(\frac{7}{5}, \frac{5}{3}, \frac{9}{7}\)
2. \(\frac{5}{3}, \frac{7}{5}, \frac{9}{7}\)
3. \(\frac{5}{3}, \frac{7}{5}, \frac{7}{5}\)
4. \(\frac{7}{5}, \frac{5}{3}, \frac{7}{5}\)

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. \(\frac{3}{8}N_ak_B(T_2-T_1)\)

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 ratio of the specific heats \(\frac{{C}_{{P}}}{{C}_{{V}}}=\gamma\)  in terms of degrees of freedom(\(n\)) is given by:

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

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. \( \frac{1}{\sqrt{2} n \pi \mathrm{d}}\)

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. \(0.5~\text{kg/m}^{3}\)

For hydrogen gas \(C_P-C_V=a\) and for oxygen gas \(C_P-C_V=b\) where molar specific heats are given. So the relation between \(a\) and \(b\) is given by: (where \(C_p\) and \(C_V\) in J mol^-1 K^-1)
1. \(a=16b\)
2. \(b=16a\)
3. \(a=4b\)
4. \(a=b\)

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

1. (a), (c)
2. (a), (d)
3. (c), (d)
4. (a), (b)