Question

The unit of specific heat is:
$A.ca{l^ \circ }C \\\ B.cal/{g^ \circ }C \\\ C.cal/g \\\ D.cal \\\$

Answer 1

There are two kinds of properties of matter: Extensive and Intensive. Extensive properties are those properties that change with the quantity of matter when increased or decreased. Intensive properties are those that do not change when there is addition or removal of matter in the system.

Complete step-by-step answer:
Before we get to the unit of specific heat, it is important that we understand the basic definition of heat capacity.
The heat capacity of a material is defined as the rate of change of heat energy in the system when there is a change in the temperature.
$C = \dfrac{{\Delta Q}}{{\Delta t}}$
Traditionally, the unit used to measure the heat capacity in chemical reactions and nutritional fields is Calories.
1 calorie is defined as the heat capacity of 1 gram of water. Basically, it means that the energy required to raise the temperature of 1 gram of water by ${1^ \circ }C$
In SI system, $1cal = 4.184 \approx 4.2J$(joules)
Heat capacity is an extensive property and its corresponding intensive property is called specific heat capacity.
So –
Heat capacity = Mass $\times$ Specific heat capacity
$C = m \times {C_p} \\\ \dfrac{{\Delta Q}}{{\Delta t}} = m{C_p} \\\ \to {C_p} = \dfrac{{\Delta Q}}{{m\Delta t}} \\\$
Substituting the units, we have –
${C_p} = \dfrac{{\Delta Q}}{{m\Delta t}} \\\ {C_p} = \dfrac{{cal}}{{{g^ \circ }C}} \\\$
${C_p} = cal/{g^ \circ }C$
Therefore, the unit of the specific heat capacity is $cal/{g^ \circ }C$

The correct option is Option B.

Note: It is an important fact to remember that whenever there is the presence of the prefix specific, it always means that the unit following it will be applicable for unit mass. Examples are specific volume, specific heat capacity, specific boiling point etc.
Also, the units of specific heat capacity in other systems are:
In SI system, it is $J{K^{ - 1}}k{g^{ - 1}}$
In countries like the USA, industries like construction, civil engineering, and chemical engineering, they use another unit called $BTU/\left( {^ \circ F} \right)\left( {lb} \right)$ where 1 BTU = 1055.06 J.