Question

A gas satisfies the relation $p V^{5 / 3}=k$, where is pressure, $V$ is volume and $k$ is constant. The dimension of constant $k$ are

• A. $\left[ ML ^{4} T ^{-2}\right]$
• B. $\left[ ML ^{2} T ^{-2}\right]$
• C. $\left[ ML ^{6} T ^{-2}\right]$
• D. $\left[ MLT ^{-2}\right]$

Answer 1

Answer: (A)

Given, $p V^{5 / 3}=k$
Using dimensional balance method
Dimension of $p= ML ^{-1} T ^{-2}$
Dimension of $V= L ^{3}$
$\Rightarrow $ Dimension of $V^{5 / 3}= L ^{5}$
As, dimension of $LHS =$ Dimension of RHS
So, dimension of $k=\left[ ML ^{-1} T ^{-2}\right] \times\left[ L ^{5}\right]=\left[ ML ^{4} T ^{-2}\right]$