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Question: The dimensions of latent heat are – \(A)\text{ }{{M}^{0}}{{L}^{2}}{{T}^{-2}}\) \(B)\text{ }{{M...

The dimensions of latent heat are –
A) M0L2T−2A)\text{ }{{M}^{0}}{{L}^{2}}{{T}^{-2}}
B) M0L1T−2B)\text{ }{{M}^{0}}{{L}^{1}}{{T}^{-2}}
C) M2L0T−2C)\text{ }{{M}^{2}}{{L}^{0}}{{T}^{-2}}
D) M0L−2T−2D)\text{ }{{M}^{0}}{{L}^{-2}}{{T}^{-2}}

Explanation

Solution

This problem can be solved by using the definition of latent heat in terms of the heat involved in the phase change of a body and its mass. By writing the dimensions of the physical quantities in the mathematical definition for latent heat, we can get the required dimensions for latent heat.

Formula used:
L=HmL=\dfrac{H}{m}

Complete step-by-step answer:
We will write the mathematical definition of latent heat and using the dimensions of the physical quantities involved in the equation, get the required dimensional formula for latent heat.
The latent heat LL of a body undergoing a phase change is the heat energy HH that is released or absorbed by a body of mass mm per unit mass.
L=HmL=\dfrac{H}{m} --(1)
Now, let us write the dimensions of the physical quantities on the right hand side of equation (1).
[L]=[Hm]=[H][m]\left[ L \right]=\left[ \dfrac{H}{m} \right]=\dfrac{\left[ H \right]}{\left[ m \right]} --(2)
Now, heat is nothing but a form of energy. Therefore, it will have the same dimensional formula as that of energy. The dimensional formula for energy is ML2T−2M{{L}^{2}}{{T}^{-2}}.
∴[H]=ML2T−2\therefore \left[ H \right]=M{{L}^{2}}{{T}^{-2}} --(3)
Now, the dimensional formula of mass is simply ML0T0M{{L}^{0}}{{T}^{0}}.
∴[m]=ML0T0\therefore \left[ m \right]=M{{L}^{0}}{{T}^{0}} --(4)
Therefore, putting (3) and (4) in (2), we get
[L]=ML2T−2ML0T0=M1−1L2−0T−2−0=M0L2T−2\left[ L \right]=\dfrac{M{{L}^{2}}{{T}^{-2}}}{M{{L}^{0}}{{T}^{0}}}={{M}^{1-1}}{{L}^{2-0}}{{T}^{-2-0}}={{M}^{0}}{{L}^{2}}{{T}^{-2}}
Hence, we have got the required dimensional formula for latent heat.

So, the correct answer is “Option A”.

Note: Students must not get confused and think that latent heat of vaporization and latent heat of fusion must have different dimensional formulae. Both of them are essentially latent heats involved during phase change. The only difference is that latent heat of fusion comes into action when there is a phase change between a solid and a liquid whereas the latent heat of vaporization comes into action when there is a phase change between the liquid state and the vapor state.