## As shown schematically in the figure , two vessels contain water solution (temperature T) of potassium permanganate ….

Q: As shown schematically in the figure , two vessels contain water solution (temperature T) of potassium Permanganate (KMnO4) of different concentration n1 and n2 (n1 >n2) molecules per unit volume with Δn =(n1-n2) << n1 . When they are connected by a tube of small length l and cross-sectional area S , KMnO4 starts to diffuse from left to right vessel through the tube . Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion . The speed v of molecules is limited by the viscous force -β v on each molecule , where β is constant . Neglecting all terms of the order (Δn)^2 , Which of the following is/are correct ? (kB is the Boltzmann constant) (a) the force causing the molecules to move across the tube is Δn kB T S

(b) force balance implies n1βvl = Δn kB T

(c) total number of molecules going across the tube per sec is $(\frac{\Delta n}{l}) (\frac{k_B T}{\beta})S$

(d) rate of molecules getting transferred through the tube does not change with time

Ans: (a,b,c)

Solution: n1 >> (n1-n2) = Δn

$p_1 = \frac{n_1 R T}{N_A}$ and $p_2 = \frac{n_2 R T}{N_A}$

$F = (n_1 -n_2)k_B T S = \Delta n k_B T S$

$V = \frac{\Delta n k_B T S}{\beta}$

$\Delta n k_B T S = l n_1 S \beta v$

$n_1 \beta v l = \Delta n k_B T$

Total number of molecules/second $= \frac{(n_1 v dt)S}{dt}$

$= n_1 v S = \frac{\Delta n K_B T v S}{\beta v l}$

$= (\frac{\Delta n}{l}) (\frac{k_B T}{\beta})S$

As Δn will decrease with time , therefore rate of molecules getting transfer decreases with time

## Consider a collection of a large number of particles each with speed v. The direction of velocity is randomly distributed in the collection….

Q: Consider a collection of a large number of particles each with speed v. The direction of velocity is randomly distributed in the collection. What is the magnitude of the relative velocity between a pairs in the collection

(a) 2V/π

(b) V/ π

(c) 8V/ π

(d) 4V/ π

Ans: (d)

## The absolute zero is the temperature at which

Q: The absolute zero is the temperature at which

(a) Water freezes

(b) All substance exist in solid state

(c) Molecular motion ceases

(d) None of the above

Ans: (c)

## The temperature at which the r.m.s. speed of hydrogen molecules is equal to escape velocity on earth surface, will be

Q: The temperature at which the r.m.s. speed of hydrogen molecules is equal to escape velocity on earth surface, will be

(a) 1060 K

(b) 5030 K

(c) 8270 K

(d) 10063 K

Ans: (d)

## The root mean square speed of the molecules of a diatomic gas is v. When the temperature is doubled ….

Q: The root mean square speed of the molecules of a diatomic gas is v. When the temperature is doubled, the molecules dissociate into two atoms. The new root mean square speed of the atom is

(a) √2 v

(b) v

(c) 2 v

(d) 4 v

Ans: (c)

## N molecules each of mass m of gas A and 2 N molecules each of mass 2 m of gas B are contained in the same vessel at temperature T….

Q: N molecules each of mass m of gas A and 2 N molecules each of mass 2 m of gas B are contained in the same vessel at temperature T. The mean square of the velocity of molecules of gas B is v2 and the mean square of x component of the velocity of molecules of gas A is w2 . The ratio w2/v2 is

(a) 1

(b) 2

(c) 1/3

(d) 2/3

Ans: (d)

## The mean free path of molecules of a gas, (radius r) is inversely proportional to

Q: The mean free path of molecules of a gas, (radius r) is inversely proportional to

(a) r

(b) √r

(c) r3

(d) r2

Ans: (d)

## Which one of the following is not an assumption of kinetic theory of gases

Q: Which one of the following is not an assumption of kinetic theory of gases

(a) The volume occupied by the molecules of the gas is negligible

(b) The force of attraction between the molecules is negligible

(c) The collision between the molecules are elastic

(d) All molecules have same speed

Ans: (d)

## At room temperature, the r.m.s. speed of the molecule certain diatomic gas is found to be 1930 m/s. The gas is

Q: At room temperature, the r.m.s. speed of the molecule certain diatomic gas is found to be 1930 m/s. The gas is

(a) H2

(b) F2

(c) O2

(d) Cl2

Ans: (a)

## A cubical box with porous walls containing an equal number of O2 and H2 molecules is placed in a large evacuated chamber….

Q: A cubical box with porous walls containing an equal number of O2 and H2 molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature T. The ratio of vrms of O2 molecules to that of the vrms, of H2 molecules, found in the chamber outside the box after a short interval is

(a) 1/2√2

(b) 1/4

(c)1/√2

(d) √2