Question

The equation of state of a gas is given by $\left(P+\frac{a}{V^3}\right)\left(V-b^2\right)=cT$, where $P$, $V$, $T$ are pressure, volume and temperature respectively, and $a$, $b$, $c$ are constants. The dimensions of $a$ and $b$ are respectively

• A. $[M{L}^8{T}^{-2}]$ and $[L^{3/2}]$
• B. $[M{L}^5{T}^{-2}]$ and $[L^3]$
• C. $[M{L}^5{T}^{-2}]$ and $[L^6]$
• D. $[M{L}^6{T}^{-2}]$ and $[L^{3/2}]$

Answer 1

Answer: (A)

$[P]=\left[\frac{a}{V^3}\right]$
$\Rightarrow \left[M{L}^{-1}{T}^{-2}\right]=\frac{a}{{\left[L^3\right]}^3}$
$\Rightarrow a=\left[M{L}^8{T}^{-2}\right]$
$[M]=\left[b^2\right]$
$\Rightarrow \left[L^3\right]=b^2$
$\Rightarrow b=\left[L^{3/2}\right]$