The volume and temperature graph is given in the figure below. If pressures for the two processes are different, then which one,  of the following, is true?

          

1.	\(P_1=P_2\) and \(P_3=P_4\) and \(P_3>P_2\)
2.	\(P_1=P_2\) and \(P_3=P_4\) and \(P_3<P_2\)
3.	\(P_1=P_2\) \(=\) \(P_3=P_4\)
4.	\(P_1>P_2\) \(>\) \(P_3>P_4\)

 

The root mean square velocity of the molecules of a gas is 300 m/s. What will be the root mean square speed of the molecules if the atomic weight is doubled and absolute temperature is halved?

The ratio of ${\mathrm{v}}_{\mathrm{rms}}:{\mathrm{v}}_{\mathrm{mp}}:{\mathrm{v}}_{\mathrm{avg}}$ is: (symbols have their usual meaning)

$1. \sqrt{3}:\sqrt{2}:\sqrt{\frac{\mathrm{\pi }}{8}}$
$2. \sqrt{3}:\sqrt{2}:\sqrt{\frac{8}{3}}$
$3. \sqrt{3}:\sqrt{\frac{8}{\mathrm{\pi }}}:\sqrt{2}$
$4. \sqrt{3}:\sqrt{2}:\sqrt{\frac{8}{\mathrm{\pi }}}$

Two chambers of different volumes, one containing ${\mathrm{m}}_1$g of a gas at pressure ${\mathrm{P}}_1$ and other containing ${\mathrm{m}}_2$g of the same gas at pressure ${\mathrm{P}}_2$ are joined to each other. If the temperature of the gas remains constant, the common pressure reached is:

1.  $\frac{{\mathrm{m}}_1{\mathrm{P}}_1+{\mathrm{m}}_2{\mathrm{P}}_2}{{\mathrm{m}}_1 + {\mathrm{m}}_2}$

2.  $\frac{{\mathrm{m}}_1{\mathrm{P}}_2+{\mathrm{m}}_2{\mathrm{P}}_1}{{\mathrm{m}}_1 + {\mathrm{m}}_2}$

3.  $\frac{{\mathrm{m}}_1{\mathrm{P}}_2+\left({\mathrm{P}}_1+{\mathrm{P}}_2\right)}{{{\mathrm{m}}^2}_1 + {\mathrm{m}}_2}$

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

At a pressure of 24 × 10⁵ dyne/cm², the volume of O₂ is 10 litre and mass is 20g. The rms velocity will be:

The rms speed of oxygen atoms is v. If the temperature is halved and the oxygen atoms combine to form oxygen molecules, then the rms speed will be:

1. $\frac{v}{\sqrt{2}}$

2. $v\sqrt{2}$

3. 2v

4. $\frac{v}{2}$

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

If \(V_\text{H}\),$$\(V_\text{N}\) and \(V_\text{O}\) denote the root-mean square velocities of molecules of hydrogen, nitrogen and oxygen respectively at a given temperature, then:
1. \(V_\text{N}>V_\text{O}>V_\text{H}\)
2. \(V_\text{H}>V_\text{N}>V_\text{O}\)
3. \(V_\text{O}>V_\text{N}>V_\text{H}\)
4. \(V_\text{O}>V_\text{H}>V_\text{N}\)

If the ratio of vapour density for hydrogen and oxygen is \(1 \over 16\), then under constant pressure, the ratio of their rms velocities will be:

What is the velocity of a wave in a monoatomic gas having pressure 1 kilopascal and density $2.6 \mathrm{kg}/{\mathrm{m}}^3$ ?

1.  $3.6 \mathrm{m}/\mathrm{s}$                                 

2.  $8.9\times {10}^3 \mathrm{m}/\mathrm{s}$

3.  Zero                                       

4.  None of these