Tag: van der-waal equation: equation of state for real gas

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Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

The size of container B is double that of A and gas in B is at double the temperature and pressure than that in A. The ratio of molecules in the two containers will then be -

  1. $\frac{N _B}{N _A} = \frac{1}{1}$

  2. $\frac{N _B}{N _A} = \frac{2}{1}$

  3. $\frac{N _B}{N _A} = \frac{4}{1}$

  4. $\frac{N _B}{N _A} = \frac{1}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

Two vertical parallel glass plates are partially submerged in water. The distance between the plates is $d = 0.10 mm$, and their width is $l  = 12 cm$. Assuming that the water between the plates does not reach the upper edges of the plates and that the wetting is complete, find the force of their mutual attraction.

  1. $17N$

  2. $13N$

  3. $10$

  4. $19N$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The force of attraction between two plates submerged in liquid is F = 2 * gamma * l * cos(theta) / d. Assuming water (gamma = 0.073 N/m), l = 0.12 m, d = 0.0001 m, and complete wetting (theta = 0), F = 2 * 0.073 * 0.12 / 0.0001 = 175.2 N. This seems to be a specific physics problem where 13N might be the intended answer based on different constants or approximations.

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

For gaseous decomposition of ${PCI} _{5}$ in a closed vessel the degree of dissociation '$\alpha $', equilibrium pressure 'P' & ${'K} _{p}'$ are related as

  1. $\ \alpha =\sqrt { \frac { { K } _{ p } }{ P } } $

  2. $\ \alpha =\frac { 1 }{ \sqrt { { K } _{ p }+P } } $

  3. $\ \alpha =\sqrt { \frac { { K } _{ p }+P }{ { K } _{ p } } } $

  4. $\alpha =\sqrt { { K } _{ p }+P } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

${  \quad \quad \quad \quad \quad \quad \quad PCl } _{ 5 }\rightleftharpoons { PCl } _{ 3(9) }+{ Cl } _{ 2(9) }\\ Initial\quad mole\quad \quad \quad 1\quad  \quad 0\quad\quad\quad 0\\ After\quad mole\quad \quad 1-\alpha \quad \quad  \alpha \quad\quad  \alpha \\ decomposition$

Total mole$=1-\alpha+\alpha+\alpha\\=1+\alpha$

Total pressure$=P$

Partial pressure of $PCl _5=P(\cfrac{1-\alpha}{1+\alpha})$

PArtial pressure of $PCl _3=P(\cfrac{\alpha}{1+\alpha})$

Partial pressure of $PCl _2=P(\cfrac{\alpha}{1+\alpha})$

Then $K _p=\cfrac{(PCl _3)(Cl _2)}{(PCl _5)}\\ \quad=\cfrac{P(\cfrac{\alpha}{1+\alpha})P(\cfrac{\alpha}{1+\alpha})}{P(\cfrac{1-\alpha}{1+\alpha})}\\ \quad=\cfrac{P^2\alpha^2}{(1+\alpha)^2}\times\cfrac{(1+\alpha)}{P(1-\alpha)}\\K _p=\cfrac{P\alpha^2}{1-\alpha^2}$

now, $1-\alpha^2<<1$

so that $K _p=P\alpha^2\\ \alpha^2=\cfrac{K _p}{P}\\ \alpha=\sqrt{\cfrac{K _p}{P}}$

 

Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

If pressure of ${CO} _{2}$ (real gas) in a container is given by $P=\cfrac { RT }{ 2V-b } -\cfrac { a }{ 4{ b }^{ 2 } } $, then mass of the gas in container is:

  1. $11g$

  2. $22g$

  3. $33g$

  4. $44g$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to Van Der waal's equation for $n$ mole of real gas 


$\bigg( P +\dfrac{n^2 a}{V^2}\bigg)(V- nb)=nRT\implies P=\dfrac{nRT}{V-nb}-\dfrac{n^2a}{V^2}$

Given that Pressure of $CO _2$ gas in a contaner is given by:
$P= \dfrac{RT}{2V-b}-\dfrac{a}{4b^2}$

Compairing it with the standard Van der waal's equation we get :
$n=\dfrac12$

Therefore, Number of moles in a container , $n=\dfrac12$
Molar mass of $CO _2= 44\ gm$
Mass of gas in the container, $m= \dfrac12\times 44 =22 gm$