Physics

# The dimensions of latent heat are -

$M ^ { 0 } L ^ { 2 } T ^ { - 2 }$

##### SOLUTION

$Latent\, heat (L)=\dfrac{Heat}{Mass}$  . . . . . . (1)

The dimensional formula of mass $=[M^1L^0T^0]$. . . . (2)

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

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

And, the dimensional formula of,

Displacement $= [M^0L^1T^0]$. . . (4)

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

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

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

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

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

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

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

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Single Correct Medium Published on 18th 08, 2020
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