A balloon contains $500<mspace\; width="1em"></mspace>{\mathrm{m}}^3$ of helium at 27°C and 1 atmosphere pressure. The volume of the helium at – 3°C temperature and 0.5 atmosphere pressure will be :

1.  $500<mspace\; width="1em"></mspace>{\mathrm{m}}^3$                                 

2.  $700<mspace\; width="1em"></mspace>{\mathrm{m}}^3$

3.  $900<mspace\; width="1em"></mspace>{\mathrm{m}}^3$                                 

4. $1000<mspace\; width="1em"></mspace>{\mathrm{m}}^3$

A given mass of a gas is allowed to expand freely until its volume becomes double. If ${\mathrm{C}}_{\mathrm{b}}$ and ${\mathrm{C}}_{\mathrm{a}}$ are the velocities of sound in this gas before and after expansion respectively, then ${\mathrm{C}}_{\mathrm{a}}$ is equal to :

1. $2{\mathrm{C}}_{\mathrm{b}}$                                 

2. $\sqrt{2}{\mathrm{C}}_{\mathrm{b}}$

3. ${\mathrm{C}}_{\mathrm{b}}$                                   

4. $\frac{1}{\sqrt{2}}{\mathrm{C}}_{\mathrm{b}}$

The molecular weight of a gas is 44. The volume occupied by 2.2 g of this gas at $0°\mathrm{C}$ and 2 atm pressure will be-

1.  0.56 litre                           

2.  1.2 litres

3.  2.4 litres                           

4.  5.6 litres

In the relation $\mathrm{n}=\frac{\mathrm{PV}}{\mathrm{RT}},<mspace\; width="1em"></mspace>\mathrm{n}=$

1.  Number of molecules                             

2.  Atomic number

3.  Mass number                                         

4.  Number of moles

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

Three containers of the same volume contain three different gases. The masses of the molecules are ${\mathrm{m}}_1,<mspace\; width="1em"></mspace>{\mathrm{m}}_2$ and ${\mathrm{m}}_3$ and the number of molecules in their respective containers are ${\mathrm{N}}_1,<mspace\; width="1em"></mspace>{\mathrm{N}}_2$ and ${\mathrm{N}}_3$ . The gas pressure in the containers are ${\mathrm{P}}_1,<mspace\; width="1em"></mspace>{\mathrm{P}}_2$ 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. $\mathrm{P}>\left({\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3\right)$

Two thermally insulated vessels 1 and 2 are filled with air at temperatures $\left({\mathrm{T}}_1,<mspace\; width="1em"></mspace>{\mathrm{T}}_2\right),$ volume $\left({\mathrm{V}}_1,<mspace\; width="1em"></mspace>{\mathrm{V}}_2\right)$ and pressure $\left({\mathrm{P}}_1,<mspace\; width="1em"></mspace>{\mathrm{P}}_2\right)$ 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. ${\mathrm{T}}_{\mathrm{c}}=\frac{8<mspace\; width="1em"></mspace>\mathrm{a}}{27<mspace\; width="1em"></mspace>\mathrm{Rb}}$                           

2. ${\mathrm{T}}_{\mathrm{c}}=\frac{\mathrm{a}}{2<mspace\; width="1em"></mspace>\mathrm{Rb}}$

3. ${\mathrm{T}}_{\mathrm{c}}=\frac{8}{27<mspace\; width="1em"></mspace>\mathrm{Rb}}$                             

4. ${\mathrm{T}}_{\mathrm{c}}=\frac{27<mspace\; width="1em"></mspace>\mathrm{a}}{8<mspace\; width="1em"></mspace>\mathrm{Rb}}$

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