A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

1.  4RT

2.  15RT

3.  9RT

4.  11RT

For an ideal gas V-T curves at constant pressure ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are shown in figure. From the figure

1. ${\mathrm{P}}_1>{\mathrm{P}}_2$

2. ${\mathrm{P}}_1<{\mathrm{P}}_2$

3. ${\mathrm{P}}_1={\mathrm{P}}_2$

4. ${\mathrm{P}}_1\le {\mathrm{P}}_2$

$4.0 ~\text g$ of a gas occupies $22.4~\text L$ at NTP. The specific heat capacity of the gas at constant volume is $5.0 ~\text{J K}^{-1}\text{mol}^{-1}.$ If the speed of sound in this gas at NTP is $952~\text{m/s}$ then the heat capacity at constant pressure is:
(Take gas constant $R=8.3 ~\text{J K}^{-1}\text{mol}^{-1}$)
1.  $8 ~\text{J K}^{-1}\text{mol}^{-1}$
2.  $7.5 ~\text{J K}^{-1}\text{mol}^{-1}$
3.  $7.0 ~\text{J K}^{-1}\text{mol}^{-1}$
4.  $8.5 ~\text{J K}^{-1}\text{mol}^{-1}$

The mean free path of gas A, with molecular diameter equal to 4 Å, contained in a vessel, at a pressure of ${10}^{–6}$ torr, is 6990 cm. The vessel is evacuated and then filled with gas B, with molecular diameter, equal to 2 Å, at a pressure of ${10}^{–3}$ torr, the temperature remaining the same. The mean free path of gas B will be

(A) 28 cm                       

(B) 280 cm

(C) 7 cm                         

(D) 14 cm

The mean free path of gas molecules depends on:
($d=$ molecular diameter)
1. $d$
2. $d^2$
3. $d^{-2}$
4. $d^{-1}$

A gas at 27°C temperature and 30 atmospheric pressure is allowed to expand to the atmospheric pressure. If the volume becomes 10 times its initial volume, then the final temperature becomes

1.  100°C                             

2.  173°C

3.  273°C                             

4.  – 173°C

The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be

1. $\mathrm{PV}=\left(5/32\right)\mathrm{RT}$                               

2. $\mathrm{PV}=5\mathrm{RT}$

3. $\mathrm{PV}=\left(5/2\right)\mathrm{RT}$                                 

4. $\mathrm{PV}=\left(5/16\right)\mathrm{RT}$

(where R is the gas constant)

At a given volume and temperature, the pressure of a gas :

1. Varies inversely as its mass

2. Varies inversely as the square of its mass

3. Varies linearly as its mass

4. Is independent of its mass

Two thermally insulated vessels $1$ and $2$ are filled with air at temperatures $\mathrm{T_1},$ $\mathrm{T_2},$ volume $\mathrm{V_1},$ $\mathrm{V_2}$ and pressure $\mathrm{P_1},$ $\mathrm{P_2}$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be: