## 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

Click to See Answer :
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

Click to See Answer :
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

Click to See Answer :
Ans: (d)