Q122 / 160 · TS EAMCET 2018 (04 May Shift 1) · Physics

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

Solution

Given, $P V^{\frac{5}{3}} = K$

Pressure $P = [{ML}^{- 1} T^{- 2}]$

Volume $V = [L^{3}]$

$\Rightarrow [{ML}^{- 1} T^{- 2}] {[L^{3}]}^{5 / 3} = K$

$∴$ Dimensions of $K = {ML}^{4} T^{- 2}$

Hence, the correct answer is option: 'A'.