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:
1. \(T_1+T_2\)

2. \(\frac{T_1+T_2}{2}\)

3. \(\frac{T_1T_2(P_1V_1+P_2V_2)}{P_1V_1T_2+P_2V_2T_1}\)

4. \(\frac{T_1T_2(P_1V_1+P_2V_2)}{P_1V_1T_1+P_2V_2T_2}\)

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. $\frac{100}{273}\mathrm{x}$

If an ideal gas has volume V at 27°C and it is heated at a constant pressure so that its volume becomes 1.5V. Then the value of final temperature will be

1. 600°C                             

2. 177°C

3. 817°C                             

4. None of these

In Boyle's law what remains constant :

1. $\mathrm{PV}$                                     

2. $\mathrm{TV}$

3. $\frac{\mathrm{V}}{\mathrm{T}}$                                     

4. $\frac{\mathrm{P}}{\mathrm{T}}$