Question

The SI unit of specific heat capacity is__________

Answer 1

Hint: To solve this question, we need to use the definition of the specific heat capacity of a body. Then we can write the expression for the heat exchanged through the substance in terms of its specific heat capacity. Finally considering the SI units of the quantities on both sides of the equation, we can get the required SI unit for the specific heat capacity.

Complete step-by-step solution:
We know that the specific heat capacity of a body is defined as the heat energy required to raise the temperature of the unit mass of the substance by $1^{\circ }C$.
Consider a body of mass m heated to raise its temperature by $\mathrm{\Delta }T$. Let its heat capacity be C and its specific heat capacity be S.
From the definition of specific heat capacity, the energy Q supplied to the body for this process can be written as
$Q=mS\mathrm{\Delta }T$
Dividing both the sides by $m\mathrm{\Delta }T$ we get
$S={\displaystyle \frac{Q}{m\mathrm{\Delta }T}}$
Now, we know that the SI unit of heat is Joule, the SI unit of mass is the kilogram, and the SI unit of temperature is Kelvin. Therefore the SI unit of the specific heat capacity, from the above relation, becomes ${\displaystyle \frac{J}{kgK}}$ or $JK{g}^{-1}{K}^{-1}$.

Note: The name of the type of heat capacity can suggest its definition. For example, the heat capacity should be the heat energy required per unit mass, because all the specific quantities are the corresponding quantity per unit mass. Likewise, there is also a kind of heat capacity known as molar heat capacity which, as its name suggests, is the heat capacity per unit mole of the substance.