Question

The dimensions of latent heat are-
(A). ${{M}^{0}}{{L}^{2}}{{T}^{-2}}$
(B). ${{M}^{0}}{{L}^{1}}{{T}^{-2}}$
(C). ${{M}^{2}}{{L}^{0}}{{T}^{-2}}$
(D). ${{M}^{0}}{{L}^{-2}}{{T}^{-2}}$

Answer 1

Heat is a form of energy. Latent heat is also called the hidden heat because it does not change the temperature of a substance. It is the heat absorbed or heat released per mole or per mass of a substance. It helps a substance to change its physical state. Dimensional formula is the representation of physical parameters in terms of fundamental units.

Formula used:
$L=\dfrac{Q}{m}$

Complete answer:
Latent heat is the energy absorbed or released during a process where temperature is constant, usually when a substance undergoes a change in its physical state that occurs without any change in temperature. For example- when ice melts, its temperature remains constant at ${{0}^{o}}\,C$. This means that ice absorbs latent heat which changes its state from solid to liquid.
Latent heat of a substance is given by-
$L=\dfrac{Q}{m}$
Here,$L$is the latent heat of the substance
$Q$is energy absorbed or energy released
$m$is the mass of the substance
We know that,
$Q=W$
Here, $W$Is work done. So, the dimensions of $Q$will be-
$[Q]=[M{{L}^{2}}{{T}^{-2}}]$ - (1)
The dimensions of mass,$m$are-
$[m]=[M]$ - (2)
Using eq (1) and eq (2), the dimensions of latent heat will be-

& [L]=\dfrac{[M{{L}^{2}}{{T}^{-2}}]}{[M]} \\\ & \Rightarrow [L]=[{{M}^{0}}{{L}^{2}}{{T}^{-2}}] \\\ \end{aligned}$$ Therefore, the dimensions of latent heat are- $$[{{M}^{0}}{{L}^{2}}{{T}^{-2}}]$$. **So the correct option is (A).** **Note:** The latent heat absorbed by a melting substance or released by a freezing substance is called the latent heat of fusion. Whereas, the heat absorbed by a substance while vaporization or released while condensation is called the latent heat of vaporization. Latent heat is used to overcome the forces between the molecules in order to change its state.