Question

The S.I. unit of specific heat capacity is:
A. $J.k{{g}^{-1}}$
B. $J.{{K}^{-1}}$
C. $J.k{{g}^{-1}}{{K}^{-1}}$
D. $kcal-k{{g}^{-1}}{{.}^{0}}{{C}^{-1}}$

Answer 1

Hint: Specific heat capacity of a substance is the amount of thermal energy absorbed or released by a body per unit mass for a unit temperature increase or decrease respectively. Hence, the unit of specific heat capacity is a complex unit of the form energy per mass per temperature. The SI unit can be found out by plugging in the SI units of these physical quantities in the proper manner.

Complete step by step answer:
The total amount of thermal energy absorbed or released by a body when its temperature increases or decreases respectively, depends upon the specific heat capacity of the body.
The specific heat capacity of a body is defined as the amount of thermal energy (heat) absorbed or released by a body per unit mass for it to have a gain or loss of unit temperature respectively. Hence, essentially,
$\text{Specific Heat Capacity = }\dfrac{\text{Total of thermal energy released or absorbed}}{\text{Total mass of the body}\times \text{Total temperature change of the body}}$
Therefore, the units for specific heat capacity should be that of $\dfrac{\text{Energy}}{\text{Mass}\times \text{Temperature}}$
The SI unit of energy is Joule $\left( J \right)$. The SI unit of mass is kilogram $\left( kg \right)$. The SI unit of temperature is Kelvin $\left( K \right)$.
Hence, the SI unit of specific heat capacity will be $\dfrac{J}{kg.K}=J.k{{g}^{-1}}{{K}^{-1}}$
Therefore, the correct option is C) $J.k{{g}^{-1}}{{K}^{-1}}$.

Note: Sometimes students get confused between specific latent heat and specific heat capacity. However, they are different. Specific latent heat is the thermal energy required by a body per unit mass for a phase change. During this time, the temperature of the body does not change. This can be remembered by understanding the meaning of the word latent which means hidden. Since, there is no temperature change involved in specific latent heat, it seems like all the heat has been hidden inside the body. Therefore, there is no relation of temperature with specific latent heat but specific heat capacity involves a unit temperature change, hence the two should not be confused.
If students had got confused, they could have marked option A) as the right answer which is the unit of specific latent heat.