## 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

Click to See Solution :
Ans: (a,b,c)

Sol: 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