The equation of state of some gases can be expressed as $(P + \frac{a}{V^{2}}) (V - b) = R T$ , where $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature , and $a$ , $b$ and $R$ are constants. The dimensions of ' $a$ ' are

Question

The equation of state of some gases can be expressed as

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

, where

P

is the pressure,

V

is the volume,

T

is the absolute temperature , and

a

,

b

and

R

are constants. The dimensions of '

a

' are

Toppr Admin · Accepted Answer

Dimension- aV2 is the same as pressure dimension is Nm-x2212-2aV2-a-m3-2-Nm-x2212-2a-Nm4-ML1T-x2212-2-MoL4To-ML5T-x2212-2-Hence- unit of a is -ML5T-x2212-2-xA0-

The equation of state of some gases can be expressed as (P+aV2)(V−b)=RT. Here P is the pressure, V is the volume, T is the absolute temperature and a,b,R are constant. The dimensions of a are:M0L6T0ML5T−2ML−1T−2M0L3T0

Dimension, aV2 is the same as pressure dimension is Nm−2aV2=a(m3)2=Nm−2a=Nm4=[ML1T−2][MoL4To]=[ML5T−2]Hence, unit of a is [ML5T−2]

Dimension, $\frac{a}{V^{2}}$ is the same as pressure dimension is $N m^{- 2}$
$\frac{a}{V^{2}} = \frac{a}{{(m^{3})}^{2}} = N m^{- 2}$
$a = N m^{4} = [M L^{1} T^{- 2}] [M^{o} L^{4} T^{o}] = [M L^{5} T^{- 2}]$
Hence, unit of $a$ is $[M L^{5} T^{- 2}]$