The root-mean-square velocity of the molecules in a sample of helium is $\frac{5}{7}th$ of that of the molecules in a sample of hydrogen.  If the temperature of the hydrogen gas is 0$°$C, that of the helium sample is about:

1. 0$°$C       

2. 5.6$°$C      

3. 273$°$C         

4. 100$°$C

The kinetic energy of one gram molecule of a gas at standard temperature and pressure is: (R = 8.31 J/mol-K)

1. 0.56 $\times {10}^4 J$             

2. $1.3\times {10}^2 J$

3. $2.7\times {10}^2 J$                 

4. $3.4\times {10}^3 J$

Gases exert pressure on the walls of containing vessel because  the gas molecules:

1. Possess momentum

2. collide with each other

3. have finite volume

4. obey gas laws

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 = $\left(\frac{5}{32}\right)RT$

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 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

An ideal gas is filled in a vessel, then

1. If it is placed inside a moving train, its temperature increases

2. Its centre of mass moves randomly

3. Its temperature remains constant in a moving car

4. None of these

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 \(O_2\)${\mathrm{}}_{}$ are shown in the figure. Choose the correct alternative: