Physics

The dimensions of latent heat are - 


ANSWER

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


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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