Question

The SI unit of specific heat capacity is __________ ( $J\,k{g^{ - 1}}\,{K^{ - 1}}$ , $J\,{K^{ - 1}}$ )

Answer 1

Hint: Recall the formula involving specific heat capacity. Then take specific heat capacity on one side and other all variables on the other side of equals to sign. Then put the SI units of all other variables. This will give the SI unit of specific heat capacity.

Complete step by step answer:
Specific heat capacity is a term related to thermodynamics. The term specific heat capacity is defined as the amount of heat energy required to raise the temperature of a unit kilogram of a substance by $1$ Kelvin.
We know that heat is a form of energy and the SI unit of energy is Joules, denoted by the symbol $J$ .
Also, we know that the SI unit of temperature is kelvin which is denoted by $K$ . Now we need to find an equation which consists of all these terms.
The required equation is given as:
$dQ = mSdT$
Where $dQ$ is the amount of heat energy required by the system to increase the temperature of a system having mass $m$ and change in temperature $dT$ .
It must be noted here that SI unit of mass is kilograms, denoted by $K$ .
Now, as we need to find the SI units of specific heat capacity, denoted above by variable $S$
We will take $S$ on one side and the other variables on the other side.
$ \Rightarrow S = \dfrac{{dQ}}{{mdT}}$
Let us put the SI units of all the variables on right hand side of the equation:
$ \Rightarrow S = \dfrac{J}{{(kg)(K)}}$
$ \Rightarrow S = J\,k{g^{ - 1}}\,{K^{ - 1}}$
This is the SI unit of specific heat capacity.

Note:
The SI unit of mass is kilogram and not gram. In such types of questions, try to find an identity or relation which relates the required unit and given units. Similar to specific heat capacity we have latent heat of fusion and latent heat of vaporization where there is no temperature change but only phase change.