Question

The equation of state of a gas is given by $(p+\frac{a}{V^3})(V-b^2)=cT$, 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. $\left[M{L}^8{T}^{-2}and{L}^{3/2}\right]$
• B. $\left[M{L}^5{T}^{-2}and{L}^3\right]$
• C. $\left[M{L}^8{T}^{-2}and{L}^6\right]$
• D. $\left[M{L}^6{T}^{-2}and{L}^{3/2}\right]$

Answer 1

Answer: (A)

$\left[M{L}^8{T}^{-2}and{L}^{3/2}\right]$

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