In the Van der Waals equation left[ P + frac{ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) According to the principle of dimensional homogeneity,only quantities with the same dimensions can be added or subtracted.$1$. From the term $\lef

Vedclass · Accepted Answer

$PV$

Vedclass · Answer

(C) According to the principle of dimensional homogeneity,only quantities with the same dimensions can be added or subtracted.$1$. From the term $\left[ P + \frac{a}{V^2} \right]$,the dimensions of $P$ must be equal to the dimensions of $\frac{a}{V^2}$.$[P] = \left[ \frac{a}{V^2} \right] \implies [a] = [P][V^2]$.$2$. From the term $[V - b]$,the dimensions of $b$ must be equal to the dimensions of $V$.$[b] = [V]$.$3$. Now,find the dimensions of the ratio $\frac{a}{b}$:$\left[ \frac{a}{b} \right] = \frac{[P][V^2]}{[V]} = [P][V]$.Therefore,the ratio $\frac{a}{b}$ is dimensionally equal to $PV$.

In the Van der Waals equation $\left[ P + \frac{a}{V^2} \right] [V - b] = RT$,where $P$ is pressure,$V$ is volume,$R$ is the universal gas constant,and $T$ is temperature,the ratio of constants $\frac{a}{b}$ is dimensionally equal to:

Similar Questions

The frequency of vibration of a string is given by $\nu = \frac{p}{2l} \left[ \frac{F}{m} \right]^{1/2}$. Here $p$ is the number of segments in the string,$l$ is the length,and $F$ is the tension. The dimensional formula for $m$ will be:

$A$ and $B$ possess unequal dimensional formulas. Then,which of the following operations is not possible in any case?

The dimensions of physical quantity $X$ in the equation $\text{Force} = \frac{X}{\text{Density}}$ are given by:

Force $F$ is given by the equation $F = \frac{X}{\text{Linear density}}$. Then the dimensions of $X$ are:

If velocity of light $c$,Planck's constant $h$,and gravitational constant $G$ are taken as fundamental quantities,then express mass,length,and time in terms of dimensions of these quantities.

Vedclass Test Series

Exam Paper Generator

Online Exam Module