In Vander Waals equation $\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT$; $P$ is pressure, $V$ is volume, $R$ is universal gas constant and $T$ is temperature. The ratio of constants $\frac{a}{b}$ is dimensionally equal to .................
$\frac{P}{V}$
$\frac{ V }{ P }$
$PV$
$PV ^{3}$
Identify the pair whose dimensions are equal
The dimensions of $K$ in the equation $W = \frac{1}{2}\,\,K{x^2}$ is
Frequency is the function of density $(\rho )$, length $(a)$ and surface tension $(T)$. Then its value is
Plane angle and solid angle have :
The workdone by a gas molecule in an isolated system is given by, $W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature, $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be