For a gas, if the ratio of  specific heats at constant pressure and constant volume is $\gamma$, then the value of degree of freedom is

(1) $\frac{\gamma +1}{\gamma -1}$

(2) $\frac{\gamma -1}{\gamma +1}$

(3) $\frac{(\gamma -1)}{2}$

(4) $\frac{2}{\gamma -1}$

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:

What is the ratio of temperatures ${\mathrm{T}}_1<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{T}}_2?$

1. $\sqrt{3}<mspace\; width="1em"></mspace>:\hspace{0.17em}1$

2. 3 : 1

3. 9 : 1

4. 27 : 1

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

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. ${\mathrm{P}}_1\ge {\mathrm{P}}_2$

When the gas in an open container is heated, the mean free path:
1. Increases
2. Decreases
3. Remains the same
4. Any of the above depending on the molar mass

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

An increase in the temperature of a gas-filled container would lead to: