Four particles have velocities 1, 0, 2, 3 m/s. The root mean square of the particles is (in m/s)

(A) $3.5$                                

(B) $\sqrt{3.5}$

(C) $1.5$                                

(D) $\sqrt{14/3}$

Joule-Thomson expansion of an ideal gas is an

(1) Isothermal process                             

(2) Isobaric process

(3) Isoenthalpic process                           

(4) Ideal process

The pressure-volume plot for an ideal gas at a given temperature has the form of a -

1. Straight line                               

2. Exponential curve

3. Rectangular hyperbola                 

4. U-shaped curve

The average, RMS and most probable velocities of gas molecules at STP increase in the order

(1) RMS < average velocity < most probable velocity

(2) Most probable velocity < average velocity < RMS

(3) Average velocity < RMS < most probable velocity

(4) RMS < most probable velocity < average velocity

Equal volumes of ${\mathrm{SO}}_2$ and $\mathrm{He}$ at a temperature T and pressure P are allowed to effuse through a hole. The rate of effusion of helium is

(1) Equal to the rate of effusion of ${\mathrm{SO}}_2$

(2) Four times the rate of effusion of ${\mathrm{SO}}_2$

(3) Half of the rate of effusion of ${\mathrm{SO}}_2$

(4) Twice the rate of effusion of ${\mathrm{SO}}_2$

Flask X is filled with 20 g of ${\mathrm{CH}}_4$ gas at 100 °C and another identical flask Y with 40 g ${\mathrm{O}}_2$ gas at the same temperature. The correct statement among the following is –

1. The pressure of the gases in the two flasks is identical

2. The pressure of ${\mathrm{CH}}_4$ in flask X is higher than that of ${\mathrm{O}}_2$ in flask Y

3. The pressure of ${\mathrm{CH}}_4$ in flask X is lower than that of ${\mathrm{O}}_2$ in flask Y

4. The pressure of ${\mathrm{CH}}_4$ in flask X is half that of ${\mathrm{O}}_2$ in flask Y

A certain volume of argon gas (Mol. wt. = 40) requires 45 s to effuse through a hole at a certain pressure and temperature. The same volume of another gas of unknown molecular weight requires 60s to pass through the same hole under the same conditions of temperature and pressure. The molecular weight of the gas is

(1) 53                                 

(2) 35

(3) 71                                 

(4) 120

The rms speed of a gas molecules at temperature $27<mspace\; width="1em"></mspace>\mathrm{K}$ and pressure $1.5$ bar is $1\times {10}^4$ cm/sec. If both temperature and pressure are raised three time, the rms speed of the gas will be

(A) $9<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>{10}^4$ cm/sec                                 

(B) $3<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>{10}^4$ cm/sec

(C) $\sqrt{3}<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>{10}^4$ cm/sec                               

(D) $1<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>{10}^4$ cm/sec

The rate of effusion of helium gas at a pressure of 1000 torr is 10 torr min–1 What will be the rate of effusion of hydrogen gas at a pressure of 2000 torr at the same temperature?

(A) $20<mspace\; width="1em"></mspace>\mathrm{torr}<mspace\; width="1em"></mspace>{\min }^{–1}$                             

(B) $40<mspace\; width="1em"></mspace>\mathrm{torr}<mspace\; width="1em"></mspace>{\min }^{–1}$

(C) $20\sqrt{2}<mspace\; width="1em"></mspace>\mathrm{torr}<mspace\; width="1em"></mspace>{\min }^{–1}$                        

(D) $10<mspace\; width="1em"></mspace>\mathrm{torr}<mspace\; width="1em"></mspace>{\min }^{–1}$

The van der waals' constants for a gas are : $\mathrm{a}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>4<mspace\; width="1em"></mspace>{\mathrm{lit}}^2<mspace\; width="1em"></mspace>\mathrm{atm}<mspace\; width="1em"></mspace>{\mathrm{mol}}^{–2},<mspace\; width="1em"></mspace>\mathrm{b}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>0.04<mspace\; width="1em"></mspace>\mathrm{lit}<mspace\; width="1em"></mspace>{\mathrm{mol}}^{–1}$. lts Boyle temperature is roughly

(1) ${100}^0\mathrm{C}$                        

(2) $1220<mspace\; width="1em"></mspace>\mathrm{K}$

(3) ${1220}^0\mathrm{C}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$                    

(4) $1600<mspace\; width="1em"></mspace>\mathrm{K}$