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Byju's Answer

Standard XII

Physics

Dimensional Analysis

Given that ...

Question

Given that $P = \frac{R T}{V - b} e^{\frac{- a V}{R T}} .$ The dimensional formula of $a$ is same as that of:
( $V$ $=$ volume, $T$ $=$ temperature, $P$ $=$ pressure, $R$ $=$ universal gas constant)

V

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P

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T

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R

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Solution

The correct option is C $P$
$\frac{a V}{R T} = d i m e n s i o n l e s s \Rightarrow a \propto \frac{R T}{V} - - - - - (1)$
$N o w, \frac{R T}{v - b} \propto \frac{R T}{v} \propto p (d i m e n s i o n a l l y) - - - (2)$
Hence, from (1) & (2) dimension of $a$ is same as $P$ .

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Similar questions

Q. The pressure of a gas

P = \frac{R T}{v - b} e^{⎛ ⎝ \frac{- a V}{R T} ⎞ ⎠}

. If

V

be the volume of gas,

R

be the universal gas constant and

T

be the absolute temperature then the dimensional formula of '

a

' is same as that of:

Q. In the equation

P = \frac{R T}{V - b} e^{\frac{a V}{R T}}

V = v o l u m e, P = p r e s s u r e, R =

universal gas constant, and

T =

temperature
The dimensional formula of

a

is same as that of

Q. The dimensions of '

a

' in Vanderwaal's equation

(P + \frac{a}{V^{2}}) (V - b) = R T

is:

(

V

-volume,

P

-Pressure,

R

-Universal gas constant,

T

- Temperature)

Select the correct formula :

(where k=Boltzmann's constant, R= gas constant, n= moles, r = density, M= molecular weight, p= pressure, T= kelvin temperature, V= volume)

a) k=RN $_{a v}$

b) $r = \frac{n M}{V}$

c) $\frac{p}{r} = \frac{R T}{M}$

d) R=kN $_{a v}$

Q. Find dimensions of constants

a

and

b

in equation.

(P + \frac{a}{V^{2}}) (V - b) = R T

, where

P

is pressure and

V

is volume,

R

is universal gas constant,

T

is temperature.

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Given that P=RTV−be−aVRT. The dimensional formula of a is same as that of:(V = volume, T = temperature, P = pressure, R = universal gas constant)

The correct option is C PaVRT=dimensionless⇒a∝RTV−−−−−(1)Now,RTv−b∝RTv∝p(dimensionally)−−−(2)Hence, from (1) & (2) dimension of a is same as P.

Given that $P = \frac{R T}{V - b} e^{\frac{- a V}{R T}} .$ The dimensional formula of $a$ is same as that of:
( $V$ $=$ volume, $T$ $=$ temperature, $P$ $=$ pressure, $R$ $=$ universal gas constant)

The correct option is C $P$
$\frac{a V}{R T} = d i m e n s i o n l e s s \Rightarrow a \propto \frac{R T}{V} - - - - - (1)$
$N o w, \frac{R T}{v - b} \propto \frac{R T}{v} \propto p (d i m e n s i o n a l l y) - - - (2)$
Hence, from (1) & (2) dimension of $a$ is same as $P$ .