Question 67: Units , Dimensions and Error Analysis

Question

The dimensional formula of latent heat is :

Accepted Answer

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] $

Answer

$$\left[\mathrm{M}^{\mathrm{0}} \mathrm{LT}^{-2}\right]$$

Answer

$$\left[\mathrm{MLT}^{-2}\right]$$

Answer

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

Answer

$$\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$$

Units , Dimensions and Error Analysis

The dimensional formula of latent heat is :

Choose the correct answer: