Question

The dimensional formula for latent heat is
(A) ${M^1}L{T^{ - 2}}$
(B) ${M^1}{L^2}{T^{ - 2}}$
(C) ${M^0}{L^2}{T^{ - 2}}$
(D) ${M^1}{L^1}{T^{ - 1}}$

Answer 1

Hint: In order to calculate dimensional formula for latent heat, first we have to calculate the dimensional formula for heat $(Q)$ and mass $(M)$ in turns of fundamental quantities. After then put the value in following formula -
Latent heat $(L) = \dfrac{{Heat(Q)}}{{Mass(m)}}$
i.e., the ratio of heat and mass of substance.

Complete step by step solution:
To calculate the dimensional formula for latent heat we use following formula
$L = \dfrac{Q}{m}$ …..(1)
Where
L $ = $ Latent heat
Q $ = $ Heat
m $ = $ mass of substance
We must write each physical quantity use in its dimensional form –
Q (Heat) which is the form of energy.
So, the dimensions of heat $ = $ dimensions of energy $ = $ dimensions of work …..(2)
Since, Work $ = $ force $ \times $ displacement …..(3)
The dimensions formula of
Force $ = m \times a = [{M^1}{L^1}{T^{ - 2}}]$ …..(4)
Displacement $ = [{M^0}{L^1}{T^0}]$ …..(5)
So, the dimension of work $ = [{M^1}{L^2}{T^{ - 2}}]$
Hence, the dimension of heat $ = [{M^1}{L^2}{T^{ - 2}}]$ …..(6)
So, from Equation (1) & (6),
The dimensional formula for latent heat is
$L = \dfrac{{[{M^1}{L^2}{T^{ - 2}}]}}{{[{M^1}]}}$
$L = [{M^0}{L^2}{T^{ - 2}}]$

So, option C is correct answer ${M^0}{L^2}{T^{ - 2}}$

Note: In order to calculate the dimensional formula of any physical quantity, we must know about the dimensions of fundamental physical quantities i.e,. mass, length, time etc.