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. $\frac{\mathrm{P}}{\mathrm{T}}$

Equation of gas in terms of pressure (P), absolute temperature (T) and density (d) is :

1. $\frac{{\mathrm{P}}_1}{{\mathrm{T}}_1{\mathrm{d}}_1}=\frac{{\mathrm{P}}_2}{{\mathrm{T}}_2{\mathrm{d}}_2}$                                 

2. $\frac{{\mathrm{P}}_1{\mathrm{T}}_1}{{\mathrm{d}}_1}=\frac{{\mathrm{P}}_2{\mathrm{T}}_2}{{\mathrm{d}}_2}$

3. $\frac{{\mathrm{P}}_1{\mathrm{d}}_2}{{\mathrm{T}}_1}=\frac{{\mathrm{P}}_2{\mathrm{d}}_1}{{\mathrm{T}}_1}$                                 

4. $\frac{{\mathrm{P}}_1{\mathrm{d}}_1}{{\mathrm{T}}_1}=\frac{{\mathrm{P}}_2{\mathrm{d}}_2}{{\mathrm{T}}_2}$

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. $3 \mathbf{:} 4$

Two vessels having equal volume contain molecular hydrogen at one atmosphere and helium at two atmospheres respectively. If both samples are at the same temperature, the mean velocity of hydrogen molecules is

1. Equal to that of helium                           

2. Twice that of helium

3. Half that of helium                                 

4. $\sqrt{2}$ times that of helium

The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K, the root mean square velocity of the gas molecules is v, at 480 K it becomes

1.  4v                                 

2.  2v

3.  v/2                               

4.  v/4

The value of densities of two diatomic gases at constant temperature and pressure are ${\mathrm{d}}_1$ and ${\mathrm{d}}_2 ,$ then the ratio of the speed of sound in these gases will be :

1. ${\mathrm{d}}_1{\mathrm{d}}_2$                                   

2. $\sqrt{{\mathrm{d}}_2/{\mathrm{d}}_1}$

3. $\sqrt{{\mathrm{d}}_1/{\mathrm{d}}_2}$                             

4. $\sqrt{{\mathrm{d}}_1{\mathrm{d}}_2}$