Two thermally insulated vessels 1 and 2 are filled with air at temperatures $\left({\mathrm{T}}_1, {\mathrm{T}}_2\right),$ volume $\left({\mathrm{V}}_1, {\mathrm{V}}_2\right)$ and pressure $\left({\mathrm{P}}_1, {\mathrm{P}}_2\right)$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

1. ${\mathrm{T}}_1+{\mathrm{T}}_2$                               

2. $\left({\mathrm{T}}_1+{\mathrm{T}}_2\right)/2$

3. $\frac{{\mathrm{T}}_1{\mathrm{T}}_2\left({\mathrm{P}}_1{\mathrm{V}}_1+{\mathrm{P}}_2{\mathrm{V}}_2\right)}{{\mathrm{P}}_1{\mathrm{V}}_1{\mathrm{T}}_2+{\mathrm{P}}_2{\mathrm{V}}_2{\mathrm{T}}_1}$                 

4. $\frac{{\mathrm{T}}_1{\mathrm{T}}_2\left({\mathrm{P}}_1{\mathrm{V}}_1+{\mathrm{P}}_2{\mathrm{V}}_2\right)}{{\mathrm{P}}_1{\mathrm{V}}_1{\mathrm{T}}_2+{\mathrm{P}}_2{\mathrm{V}}_2{\mathrm{T}}_2}$

The value of critical temperature in terms of Vander Waal’s constant a and b is

1. ${\mathrm{T}}_{\mathrm{c}}=\frac{8 \mathrm{a}}{27 \mathrm{Rb}}$                           

2. ${\mathrm{T}}_{\mathrm{c}}=\frac{\mathrm{a}}{2 \mathrm{Rb}}$

3. ${\mathrm{T}}_{\mathrm{c}}=\frac{8}{27 \mathrm{Rb}}$                             

4. ${\mathrm{T}}_{\mathrm{c}}=\frac{27 \mathrm{a}}{8 \mathrm{Rb}}$

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. $\frac{100}{273}\mathrm{x}$

A tyre kept outside in sunlight bursts off after sometime because of :

1. Increase in pressure                                 

2. Increases in volume

3. Both (a) and (b)                                       

4. None of these

The respective speeds of the molecules are 1, 2, 3, 4 and 5 km/sec. The ratio of their r.m.s. velocity and the average velocity will be

1. $\sqrt{11} \mathbf{:} 3$                                   

2. $3\mathbf{ }\mathbf{:} \sqrt{11}$

3. $1 \mathbf{:} 2$                                         

4. $3 \mathbf{:} 4$

At a given temperature the root mean square velocities of oxygen and hydrogen molecules are in the ratio

1.  16 : 1                               

2.  1 : 16

3.  4 : 1                                 

4.  1 : 4

At a given temperature if ${\mathrm{V}}_{\mathrm{rms}}$ is the root mean square velocity of the molecules of a gas and ${\mathrm{V}}_{\mathrm{s}}$ the velocity of sound in it, then these are related as $\left(\mathrm{\gamma }=\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{v}}}\right)$

1. ${\mathrm{V}}_{\mathrm{rms}}={\mathrm{V}}_{\mathrm{s}}$                             

2. ${\mathrm{V}}_{\mathrm{rms}}=\sqrt{\frac{3}{\mathrm{\gamma }}}\times {\mathrm{V}}_{\mathrm{s}}$

3. ${\mathrm{V}}_{\mathrm{rms}}=\sqrt{\frac{\mathrm{\gamma }}{3}}\times {\mathrm{V}}_{\mathrm{s}}$                   

4. ${\mathrm{V}}_{\mathrm{rms}}=\left(\frac{3}{\mathrm{\gamma }}\right)\times {\mathrm{V}}_{\mathrm{s}}$

Three containers of the same volume contain three different gases. The masses of the molecules are ${\mathrm{m}}_1, {\mathrm{m}}_2$ and ${\mathrm{m}}_3$ and the number of molecules in their respective containers are ${\mathrm{N}}_1, {\mathrm{N}}_2$ and ${\mathrm{N}}_3$ . The gas pressure in the containers are ${\mathrm{P}}_1, {\mathrm{P}}_2$ and ${\mathrm{P}}_3$ respectively. All the gases are now mixed and put in one of the containers. The pressure P of the mixture will be :

1. $\mathrm{P}<\left({\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3\right)$                               

2. $\mathrm{P}=\frac{{\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3}{3}$

3. $\mathrm{P}={\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3$                                 

4. $\mathrm{P}>\left({\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3\right)$

The equation of state corresponding to 8 g of ${\mathrm{O}}_2$ is :

1.  PV = 8RT                           

2.  PV = RT/4

3.  PV = RT                             

4.  PV = RT/2

In the relation $\mathrm{n}=\frac{\mathrm{PV}}{\mathrm{RT}}, \mathrm{n}=$

1.  Number of molecules                             

2.  Atomic number

3.  Mass number                                         

4.  Number of moles