Question

The dimensions of latent heat are -

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

Answer 1

Answer: (B)

$Latentheat\left(L\right)=\frac{Heat}{Mass}$ . . . . . . (1)

The dimensional formula of mass $=\left[M^1{L}^0{T}^0\right]$. . . . (2)

Also, the dimensions of heat $=$ dimensions of energy $=$ dimensions of work

Since, $work=force\times displacement$ . . . . (3)

And, the dimensional formula of,

Displacement $=\left[M^0{L}^1{T}^0\right]$. . . (4)

Force $=m\times a=\left[M^1{L}^1{T}^{-2}\right]$ . . . (5)

On substituting equation (4) and (5) in equation (3) we get,

Work $=\left[M^1{L}^1{T}^{-2}\right]\times \left[L^1\right]$

Therefore, the dimensions of work or heat $=\left[M^1{L}^2{T}^{-2}\right]$ . . . . (6)

On substituting equation (2) and (6) in equation (1) we get,

Or, $L=\frac{\left[M^1{L}^2{T}^{-2}\right]}{\left[M^1{L}^0{T}^0\right]}=\left[M^0{L}^2{T}^{-2}\right]$

Therefore, latent heat is dimensionally represented as $\left[M^0{L}^2{T}^{-2}\right]$