A gas satisfies the relation p V5 / 3=k, where is pressure, V is volume and k is constant. The dimension of constant k are

Question

A gas satisfies the relation p V5 / 3=k, where is pressure, V is volume and k is constant. The dimension of constant k are (A) [ ML 4 T -2] (B) [ ML 2 T -2] (C) [ ML 6 T -2] (D) [ MLT -2]

Tardigrade Admin · Accepted Answer

Given, p V5 / 3=k Using dimensional balance method Dimension of p= ML -1 T -2 Dimension of V= L 3 ⇒ Dimension of V5 / 3= L 5 As, dimension of LHS = Dimension of RHS So, dimension of k=[ ML -1 T -2] ×[ L 5]=[ ML 4 T -2]

Q. 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

$[M L^{4} T^{- 2}]$

$[M L^{2} T^{- 2}]$

$[M L^{6} T^{- 2}]$

$[M L T^{- 2}]$

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

Q. A gas satisfies the relation pV5/3=k, where is pressure, V is volume and k is constant. The dimension of constant k are

[ML4T−2]

[ML2T−2]

[ML6T−2]

[MLT−2]