QJEEM24Ph125d: JEE Main 2024 Physics - Class 11 JEEM24Ph125d Solution: The dimensional formula of latent heat is :

To derive the dimensional formula of latent heat, we need to understand what latent heat actually refers to. Latent heat is the amount of heat absorbed or released by a substance during a change in its physical state (phase) that occurs without changing its temperature.

The formula for latent heat ( $L$ ) is given by:

$Q = mL$

where:

$Q$ = Heat absorbed or released (with the dimension of energy $[\mathrm{ML}^2\mathrm{T}^{-2}]$ ),

$m$ = Mass of the substance ( $[\mathrm{M}]$ ),

$L$ = Latent heat.

To find the dimensions of latent heat, we rearrange the formula to solve for $L$ :

$L = \frac{Q}{m}$

Knowing the dimensions of $Q$ (energy, which is equivalent to work done, with dimensions $[\mathrm{ML}^2\mathrm{T}^{-2}]$ ) and $m$ (mass, with dimensions $[\mathrm{M}]$ ), we can substitute these into the equation to find $L$ 's dimensions:

$L = \frac{[\mathrm{ML}^2\mathrm{T}^{-2}]}{[\mathrm{M}]}$

This simplifies to:

$L = [\mathrm{L}^2\mathrm{T}^{-2}]$

Therefore, the dimensional formula of latent heat is:

$L = [\mathrm{M}^0 \mathrm{L}^2 \mathrm{T}^{-2}]$

So, the correct option is:

Option C $\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$