Which one of the following gases possesses the largest internal energy?

1.	\(2\) moles of helium occupying \(1 ~\text m^3\) at \(300 ~\text K\)
2.	\(56~\text{kg}\) of nitrogen at \(10^5 ~\text{Nm}^{-2}\) and \(300 ~\text K\)
3.	\(8\) grams of oxygen at \(8~\text{atm}\) and \(300 ~\text K\)
4.	\(6 \times 10^{26}\) molecules of argon occupying \(40 ~\text m^3\) at \(900 ~\text K\)

If 300 ml of a gas at 27°C is cooled to 7°C at constant pressure, then its final volume will be -

(1) 540 ml

(2) 350 ml

(3) 280 ml

(4) 135 ml

One mole of a perfect gas in a cylinder fitted with a piston has a pressure P, volume V and temperature 273 K. If the temperature is increased by 1 K keeping pressure constant, the increase in volume is

(1) $\frac{2V}{273}$

(2) $\frac{V}{91}$

(3) $\frac{V}{273}$

(4) V

Two gases of equal mass are in thermal equilibrium. If ${\mathrm{P}}_{\mathrm{a}}, {\mathrm{P}}_{\mathrm{b}}$ and ${\mathrm{V}}_{\mathrm{a}}$ and ${\mathrm{V}}_{\mathrm{b}}$ are their respective pressures and volumes, then which relation is true

1. ${\mathrm{P}}_{\mathrm{a}}\ne {\mathrm{P}}_{\mathrm{b}} ; {\mathrm{V}}_{\mathrm{a}}={\mathrm{V}}_{\mathrm{b}}$                             

2. ${\mathrm{P}}_{\mathrm{a}}={\mathrm{P}}_{\mathrm{b}} ; {\mathrm{V}}_{\mathrm{a}}\ne {\mathrm{V}}_{\mathrm{b}}$

3. $\frac{{\mathrm{P}}_{\mathrm{a}}}{{\mathrm{V}}_{\mathrm{a}}}=\frac{{\mathrm{P}}_{\mathrm{b}}}{{\mathrm{V}}_{\mathrm{b}}}$                                               

4. ${\mathrm{P}}_{\mathrm{a}}{\mathrm{V}}_{\mathrm{a}} = {\mathrm{P}}_{\mathrm{b}}{\mathrm{V}}_{\mathrm{b}}$

The mean free path of gas molecules depends on (d = molecular diameter)

1. $\mathrm{d}$                                         

2. ${\mathrm{d}}^2$

3. ${\mathrm{d}}^{-2}$                                   

4. ${\mathrm{d}}^{-1}$

For Boyle's law to hold the gas should be :

1. Perfect and of constant mass and temperature

2. Real and of constant mass and temperature

3. Perfect and at a constant temperature but variable mass

4. Real and at a constant temperature but variable mass

Consider a 1 c.c. sample of air at the absolute temperature ${\mathrm{T}}_0$ at sea level and another 1 c.c. sample of air at a height where the pressure is the one-third atmosphere. The absolute temperature T of the sample at that height is :

1. Equal to ${\mathrm{T}}_0/3$

2. Equal to $3/{\mathrm{T}}_0$

3. Equal to ${\mathrm{T}}_0$

4. Cannot be determined in terms of ${\mathrm{T}}_0$ from the above data

To double the volume of a given mass of an ideal gas at 27°C keeping the pressure constant, one must raise the temperature in degree centigrade to

1. 54°                                   

2. 270°

3. 327°                                 

4. 600°

Which of the following statements about kinetic theory of gases is wrong

1. The molecules of a gas are in continuous random motion

2. The molecules continuously undergo inelastic collisions

3. The molecules do not interact with each other except during collisions

4. The collisions amongst the molecules are of short duration

If a Vander-Waal's gas expands freely, then final temperature is

1. Less than the initial temperature

2. Equal to the initial temperature

3. More than the initial temperature

4. Less or more than the initial temperature depending on the nature of the gas