Under which of the following conditions is the law PV = RT obeyed most closely by a real gas

1. High pressure and high temperature

2. Low pressure and low temperature

3. Low pressure and high temperature

4. High pressure and low temperature

That gas cannot be liquified :

1. Which obeys Vander Waal's equation

2. Which obeys gas equation at every temperature and pressure

3. The molecules of which are having potential energy

4. Which is a inert gas

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