Question

The S.I. unit of specific heat capacity is
$\begin{align}
  & \text{A}\text{. Jk}{{\text{g}}^{-1}}{{K}^{-1}} \\
 & \text{B}\text{. Jmo}{{\text{l}}^{-1}}{{K}^{-1}} \\
 & \text{C}\text{. Jk}{{\text{g}}^{-1}} \\
 & \text{D}\text{. J}{{K}^{-1}} \\
\end{align}$

Answer 1

Hint: Convert the mathematical formula of specific heat capacity into basic units in the MKS system. The amount of heat required to change the temperature of a substance is directly proportional to the mass of the substance and change in the temperature. Constant proportion is known as specific heat. Arrange the formula and then put value in each quantity equals to 1 unit.

 Complete step by step answer:
The International System of Units (SI) is the modern form of the metric system. It is the only system of measurement with official status in nearly every country in the world. It comprises a coherent system of units of measurement starting with seven base units.
Specific heat capacity is defined as the quantity of heat required to raise the temperature of a unit mass of a substance through $1{}^{0}C(\text{or 1K})$.
The amount of heat required to change the temperature of a substance is directly proportional to the mass of the substance and change in the temperature $\Delta T.i.e$
$\begin{align}
  & Q\alpha m\vartriangle T \\
 & \text{or }Q=cm\vartriangle T \\
\end{align}$
Where $c$ is the specific heat (or specific heat capacity) of a substance.
Above equation can be written as
$c=\dfrac{Q}{m\vartriangle T}$
If $m=1kg$ and $\vartriangle \text{T=}{{\text{1}}^{0}}C$then $\text{c=Q}$
S.I. unit of specific heat is \[\text{Jk}{{\text{g}}^{-10}}C\text{ or Jk}{{\text{g}}^{-1}}{{K}^{-1}}.\]

So, the correct answer is “Option A”.

Additional Information:
In the case of a gas slight change in temperature is accompanied by considerable changes in both i.e. volume and pressure. If gas is heated at constant pressure, volume changes, and hence some work is done on surrounding in expansion. Hence more heat is required. Therefore specific heat at constant pressure is more than specific heat at constant volume. So it is necessary to define two specific heats for gas:
1) The specific heat of the gas at constant volume is defined as the quantity of heat required to raise the temperature of a unit mass of gas through $1K$ when its volume is kept constant.
2) The specific heat of the gas at constant pressure is defined as the quantity of heat required to raise the temperature of a unit mass of gas through $1K$ when its pressure is kept constant.
For the unit mass of gas, the specific heats are called principal specific heats. While defining the specific heats, if one mole of gas is considered instead of unit mass, then the specific heats are called the molar specific heats.
In C.G.S, unit is $ca{{\lg }^{-1}}{{K}^{-1\text{ }}}\text{or erg }{{\text{g}}^{-1}}{}^{0}{{C}^{-1}}.$

Note:
Students usually try to memorize the SI units, but it is a wrong way to do these types of questions. Students should only memorize the basic formulas, and they should convert the given formula into basic units to dimensional formula or SI units. c used in the question is known as specific heat as well as specific heat capacity. Though it is constant of proportionality it is a dependent quantity. It depends on mass, heat, and temperature.