Question

The equation of state of some gases can be expressed as $(P+\frac{a}{V^2})(V-b)=RT$. Here P is the pressure, $V$ is the volume, $T$ is the absolute temperature and $a,b,R$ are constant. The dimensions of $a$ are:

• A. $M{L}^5{T}^{-2}$
• B. $M{L}^{-1}{T}^{-2}$
• C. $M^0{L}^3{T}^0$
• D. $M^0{L}^6{T}^0$

Answer 1

Answer: (A)

$M{L}^5{T}^{-2}$

Dimension, $\frac{a}{V^2}$ is the same as pressure dimension is $N{m}^{-2}$

$\frac{a}{V^2}=\frac{a}{{\left(m^3\right)}^2}=N{m}^{-2}$

$a=N{m}^4=\left[M{L}^1{T}^{-2}\right]\left[M^o{L}^4{T}^o\right]=\left[M{L}^5{T}^{-2}\right]$

Hence, unit of $a$ is $\left[M{L}^5{T}^{-2}\right]$