The molecular weight of two gases is $M_1$ and $M_2.$ At any temperature, the ratio of root mean square velocities $v_1$ and $v_2$ will be:
1. $\sqrt{\frac{M_1}{M_2}}$
2. $\sqrt{\frac{M_2}{M_1}}$
3. $\sqrt{\frac{M_1+M_2}{M_1-M_2}}$
4. $\sqrt{\frac{M_1-M_2}{M_1+M_2}}$

According to the kinetic theory of gases, at absolute zero temperature: [AIIM 1998; UPSEAT 2000]

1. Water freezes                             

2. Liquid helium freezes

3. Molecular motion stops               

4. Liquid hydrogen freezes

PV versus T graphs of equal masses of $H_2$, $He$ and $O_2$ are shown in the figure. Choose the correct alternative:               

The root-mean-square speed of hydrogen molecules at 300 K is 1930 m/s. Then the root mean square speed of oxygen molecules at 900 K will be: [MH CET 2002; Odisha JEE 2010]

1. 1930$\sqrt{3}$ m/s                     

2. 836 m/s

3. 643 m/s                               

4. $\frac{1930}{\sqrt{3}}$ m/s

What is the mass of 2 liters of nitrogen at 22.4 atmospheric pressure and 273 K?

1. 28 g               

2. 14$\times 22.4$ g

3. 56 g               

4. None of these

Mean kinetic energy per degree of freedom of gas molecules is:

1. $\frac{3}{2}kT$             

2. kT             

3. $\frac{1}{2}kT$             

4. $\frac{3}{2}RT$

The temperature of an ideal gas is increased from $27°$ to $927°C$. The r.m.s. speed of its molecules becomes-

1. twice           

2. half           

3. four times         

4. one fourth

The equation $\left(p+\frac{a}{v^2}\right)\left(v-b\right)=RT$ is known as:

1. Perfect gas equation

2. Joule Thomson's equation

3. Vander Waal's equation

4. Maxwell's equation

The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be: (where R is the constant)

1. PV = 5RT

2. PV = $\left(\frac{5}{2}\right)RT$

3. PV = $\left(\frac{5}{16}\right)RT$

4. PV = $\left(\frac{5}{32}\right)RT$