$4.0 ~\text g$ 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:

In Vander Waal’s equation, a and b represent $\left(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)\left(\mathrm{v}-\mathrm{b}\right)=\mathrm{RT}$

1. Both a and b represent correction in volume

2. Both a and b represent adhesive force between molecules

3. a represents adhesive force between molecules and b correction in volume

4. a represents correction in volume and b represents adhesive force between molecules

At 0°C the density of a fixed mass of a gas divided by pressure is x. At 100°C, the ratio will be:

1. $\mathrm{x}$                                   

2. $\frac{273}{373}\mathrm{x}$

3. $\frac{373}{273}\mathrm{x}$                           

4. $\frac{100}{273}\mathrm{x}$