Question

The SI unit of specific heat capacity is \[Jk{{g}^{-1}}{{K}^{-1}}\]. What is the unit of specific heat capacity expressed in SI base units?
(A) \[m{{s}^{-2}}{{K}^{-1}}\]
(B) \[kgm{{s}^{-2}}{{K}^{-1}}\]
(C) \[{{m}^{2}}{{s}^{-2}}{{K}^{-1}}\]
(D) \[kg{{m}^{2}}{{s}^{-2}}{{K}^{-1}}\]

Answer 1

Hint: The specific heat capacity \[({{C}_{P}})\]is the amount of heat required to raise the temperature of the substance per unit mass. The SI unit of specific heat capacity is \[Jk{{g}^{-1}}{{K}^{-1}}\]. If we know the S.I unit for joule, we can substitute that value in the above value.

Complete step by step answer:
First thing is we have to understand what a specific heat is. Specific heat capacity is the amount of heat required to raise the temperature of one gram of substance by \[1{}^\circ C\]. It is given by the formula:
\[Q=Cm\Delta t\]
Where
Q=Quantity of heat absorbed
C=Specific heat capacity of the substance
m=mass of the body
\[\Delta t\]=Rise in temperature
Specific heat capacity is an extensive property. The S.I unit of specific heat capacity can be defined as the amount of heat in joules required to raise the temperature of one gram of substance by one kelvin. Its S.I unit of specific heat capacity can be expressed as\[Jk{{g}^{-1}}{{K}^{-1}}\].
Joule is the unit of work done. S.I unit of joule is \[J=kg{{m}^{2}}{{s}^{-2}}\]
S.I unit of Specific heat capacity =\[Jk{{g}^{-1}}{{K}^{-1}}\]
In order to find the base S.I unit, we have to substitute S.I unit of Joules i.e.\[J=kg{{m}^{2}}{{s}^{-2}}\] in unit of specific heat capacity.
$\implies$ \[kg{{m}^{2}}{{s}^{-2}}k{{g}^{-1}}{{K}^{-1}}\]
$\therefore$ \[{{m}^{2}}{{s}^{-2}}{{K}^{-1}}\]
SI base units of specific heat capacity is \[{{m}^{2}}{{s}^{-2}}{{K}^{-1}}\]

Therefore, the correct answer is option(C) \[{{m}^{2}}{{s}^{-2}}{{K}^{-1}}\].

Additional information:
Specific heat capacity is following Law of conservation of energy. For example, when we keep two materials having different temperatures with each other, the heat from the warmer material will flow to the colder materials until the temperature becomes the same in both the materials. Law of conservation of energy says that energy can neither be created nor destroyed but transformed from one form to another.

Note: - Water has a high specific heat capacity. It will take a lot of energy to increase the temperature of water compared to other substances. This is one of the reasons why water is used as a coolant in a car's radiator. The specific heat capacity of water is one of the important properties. The high specific heat capacity of water helps to sustain the lives of aquatic plants and animals as water takes a very long time to get heated.
- It might take around 4.184J of heat (exactly around 1 calorie) to increase the temperature of one kg of water by \[1{}^\circ C\]