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Question: The S.I unit of specific heat capacity is A. \[{\text{J}}\,\,{\text{k}}{{\text{g}}^{ - 1}}\] B. ...

The S.I unit of specific heat capacity is
A. J  kg−1{\text{J}}\,\,{\text{k}}{{\text{g}}^{ - 1}}
B. J  K−1{\text{J}}\,\,{{\text{K}}^{ - 1}}
C. J  kg−1 K−1{\text{J}}\,\,{\text{k}}{{\text{g}}^{ - 1}}\,{{\text{K}}^{ - 1}}
D. k cal−kg−1  ∘C−1{\text{k}}\,{\text{cal}} - {\text{k}}{{\text{g}}^{ - 1}}\,\,^\circ {{\text{C}}^{ - 1}}

Explanation

Solution

Specific heat capacity (or specific heat) is the heat energy required to cause rise in temperature by 1 kelvin of 1 kg mass of a substance. Use the formula for heat energy supplied or gained by the substance of mass m due to change in temperature of the substance by ΔT\Delta T to answer this question.

Complete step by step solution:
We know there are two types of specific heats: specific heat at constant pressure denoted by CP{C_P} and specific heat at constant volume denoted by CV{C_V}. We can define the specific heat as the heat required to raise the temperature of a substance of mass 1 kg by 1 Kelvin.

We have the formula for heat supplied or gained by the substance of mass m due to change in temperature of the substance by ΔT\Delta T is given as,
Q=mCΔTQ = mC\Delta T
Here, m is the mass of the substance and C is the specific heat capacity of the substance.

We rearrange the above equation as,
C=QmΔTC = \dfrac{Q}{{m\Delta T}}

We know that the S.I unit of heat energy is joule, the S.I unit of mass is kg and the S.I unit of temperature is Kelvin. Therefore, the unit of specific heat capacity will be,
C=J(kg)(K)C = \dfrac{{\text{J}}}{{\left( {{\text{kg}}} \right)\left( {\text{K}} \right)}}
⇒C=J  kg−1K−1\Rightarrow C = {\text{J}}\,\,{\text{k}}{{\text{g}}^{ - 1}}{{\text{K}}^{ - 1}}

Therefore, the unit of the specific heat capacity is J  kg−1K−1{\text{J}}\,\,{\text{k}}{{\text{g}}^{ - 1}}{{\text{K}}^{ - 1}}.

So, the correct answer is “Option C”.

Note:
To answer these types of questions, the key is to recall the formula which can best suit to determine the unit of the given physical quantity. To answer this question, you should know the unit of heat. Remember, the heat is also the energy. The S.I unit of temperature is Kelvin and not degree Celsius.