1. The mean free path l for a gas molecule depends upon diameter, d of the molecule as

(1).\(l\propto {\frac{1}{d^2}}\)

(2). \(l\propto d\)

(3). \(l\propto {d^2}\)

(4). \(l\propto {\frac{1}{d}}\)

2. An ideal gas equation can bewritten as \( p = \frac{ \rho RT}{M_0}\)where, \(\rho\) and \(M_0\) are respectively,

(1).mass density, mass of the gas

(2). number density, molar mass

(3). mass density, molar mass

(4). number density, mass of the gas

3. The mean free path l for a gas,with molecular diameter d and number density n can be expressed as

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

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

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

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

4. A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27°C.Its density is (\(R = 8.3 J mol^{ −1} K^{−1}\) )

(1).\(0.2\, kg/m^3\)

(2). \( 0.1\, kg/m^3\)

(3). \( 0.02 \, kg/m^3\)

(4). \(0.5 \, kg/m^3\)

5. Increase in temperature of a gas filled in a container would lead to

(1).increase in its kinetic energy

(2). decrease in its pressure

(3). decrease in intermolecular distance

(4). increase in its mass

6. At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere? (Given: mass of oxygen molecule,\(m = 2.76 × 10^−{26}\, kg\) ,Boltzmann’s constant\(k_B = 1.38 10^{-23} J K^{ −1}\))

(1).\(5.016 × 10^4\, K\)

(2). \(8.326 × 10^4\, K\)

(3). \(2.508 × 10^4\, K\)

(4). \(1.254 × 10^4\, K\)

7. The molecules of a given mass of a gas have r.m.s. velocity of \(200ms^{−1}\) at \(27^\circ C\) and \(1.0 × 10^5 Nm^{ −2}\) pressure. When the temperature and pressure of the gas are respectively, \(127^ \circ C\) and 0\(.05 × 10^5 Nm^{ −2}\) , the rms velocity of itsmolecules in \(ms^{ −1}\) is

(1).\(\frac{400}{\sqrt{3}}\)

(2). \(\frac{100\sqrt{2}}{3}\)

(3). \(\frac{100}{3}\)

(4). \(100\sqrt{2}\)

8. A given sample of an ideal gas occupies a volume V at a pressure p and absolute temperature T. The mass of each molecule of the gas is m.Which of the following gives the density of the gas?

(1).p / (kT)

(2). pm/ (kT)

(3). p / (kTV)

(4). mkT

9. Match Column l with Column ll andchoose the correct match fromthegiven choices.

(1).A-3, B-1, C-4, D-2

(2). A-2, B-3, C-4, D-1

(3). A-2, B-1, C-4, D-3

(4). A-3, B-2, C-1, D-4

10. The average thermal energy for a monoatomic gas is (where,\(k_ B\) is Boltzmann constant and T is absolute temperature.)

(1).\(\frac{3}{2}k_BT\)

(2). \(\frac{5}{2}k_BT\)

(3). \(\frac{7}{2}k_BT\)

(4). \(\frac{1}{2}k_BT\)

11. The value of \(\gamma =\left(\frac{C_p}{C_v}\right)\), 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).7/5, 5/3, 9/7

(2). 5/3, 7/5, 9/7

(3). 5/3, 7/5, 7/5

(4). 7/5, 5/3, 7/5

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

(1).4 RT

(2). 15 RT

(3). 9 RT

(4). 11 RT

13. One mole of an ideal monatomic gas undergoes a process described by the equation \(pV^3 = constant\). The heat capacity of the gas during this process is

(1).3/2 R

(2). 5/2 R

(3). 2R

(4). R

14. The mean free path of molecules of a gas,, (radius r) is inversly proportional to [2014]

(1).\(r^3\)

(2). \(r^2\)

(3). \(r\)

(4). \(\sqrt{r}\)

15. The following graph represents the T - V curves of an ideal gas ( where T is the temperature and V the volume ) at three pressures P1 , P2 and P3 compared with those of Charles's law represented as dotted lines .

(1).P₂ > P₁ > P₃

(2). P₁ > P₂ > P₃

(3). P₃ > P₂ > P₁

(4). P₁ > P₃ > P₂

16. The ratio of specific heats \(\displaystyle \frac{C_p}{C_v}\,=\, \gamma\) in terms of degrees of freedom (n) is given by:

(1).\(\displaystyle \left(1\,+\,\frac{1}{n} \right)\)

(2). \(\displaystyle \left(1\,+\,\frac{n}{3} \right)\)

(3). \(\displaystyle \left(1\,+\,\frac{2}{n} \right)\)

(4). \(\displaystyle \left(1\,+\,\frac{n}{2} \right)\)