Maxwell's speed distribution graph is drawn as shown below. The most probable speed of the gas molecules is:
                        
1. 4 km/s

2. Between 3 km/s and 1 km/s

3. Any value between 2 km/s and 6 km/s

4. More than 4 km/s

A closed container having an ideal gas is heated gradually to increase the temperature by 20%  The mean free path will become/remain:

1. 20% more

2. Same

3. 20% less

4. 33% less

Two ideal gases have the same number of molecules per unit volume and the radii of their molecules are \(r\) and \(3r\) respectively. The ratio of their mean free path in identical containers will be:
1. \(3:1\)
2. \(9:1\)
3. \(1:1\)
4. \(1:4\)

When the gas in an open container is heated, the mean free path:

From the following V-T diagram, we can conclude

1. ${\mathrm{P}}_1$ = ${\mathrm{P}}_2$

2. ${\mathrm{P}}_1$ > ${\mathrm{P}}_2$

3. ${\mathrm{P}}_1$ < ${\mathrm{P}}_2$

4. ${\mathrm{P}}_1\ge {\mathrm{P}}_2$

How does the temperature change when the state of an ideal gas is changed according to the process shown in the figure?

What is the ratio of temperatures ${\mathrm{T}}_1 \mathrm{and} {\mathrm{T}}_2?$

1. $\sqrt{3} :\hspace{0.17em}1$

2. 3 : 1

3. 9 : 1

4. 27 : 1

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. \(0.5~\text{kg/m}^{3}\)

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. \(\frac{1}{2}k_BT\)