Question

THE VANDER WALS' EQUATION FOR 1 MOLE OF A REAL GAS IS [P+A/V TO THE POWER OF 2 ](V-B) WHERE P IS PRESSURE , V IS THE VOLUME , T IS THE ABSOLUTE TEMPERATURE AND R IS THE MOLAR GAS CONSTANT . CHOOSE THE CORRECT ANSWER. A)THE DIMENSIONS OF B ARE [M TO THE POWER 0 L TO THE POWER 3 T TO THE POWER 0] B)THE UNIT OF A IS JOULE METRE. C)THE DIMENSIONS OF A IS [M , L TO THE POWER 5 T TO THE POWER - 2.] D)THE DIMENSION OF B IS [ M, L TO THE POWER 5 T TO THE POWER -2]​

Answer 1

Answer:-

$a = [ML^5 T ^-2]$

$b = [L^3 ]$

Option A

Given :-

$( P + \dfrac{a}{v^2} ) \times (v -b) = R \theta$

To find:-

The dimension of A and B.

Solution :-

We know that dimension formula of :-

$p = [ML^{-1}T^{-2}]$

$v = [L^3]$

Since, $R \theta$ is a dimension less quantity because it is gas constant.

Now,

By using principal of homogeneity,

$(v-b) = 0$

→$v - b = 0$

→$v = b$

→$b = [L^3 ]$

__________________________________________

$p + \dfrac{a}{v^2}= 0$

→$\dfrac{pv^2 + a}{v^2}= 0$

→$pv^2 + a = 0$

→$a = pv^2$

→$a = [ML^{-1}T^{-2} \times (L^3) ^2]$

→$a = M L^{-1 + 6}T^{-6}$

→$a = [ML^5 T ^-2]$

hence,

The value of a is $a = [ML^5 T ^-2]$ and b is $b = [L^3 ]$.