Question

State two differences between “Heat Capacity” and “Specific Heat Capacity”.

Answer 1

Hint: Heat capacity is defined as the amount of heat required to raise the temperature of the whole body (mass m) through ${{1}^{0}}$C or 1. The heat required to raise the temperature of the unit mass of a body through ${{1}^{0}}$C or 1 K is called specific heat capacity of the body.

Complete step by step answer:
Thermal capacity, also known as heat capacity, is defined as the amount of heat required to raise the temperature of the whole body (mass m) through ${{1}^{0}}$C or 1 K.
It is represented by C.
When some of heat is supplied to a body of mass m, its temperature rises. Let the change in temperature of the body be $\Delta $T and the heat energy supplied be Q. Then the relation between the heat capacity (C) of the body, the change in temperature ($\Delta $T) of the body and the supplied heat Q is given as $Q=C\Delta T$.
Therefore, $C=\dfrac{Q}{\Delta T}$.
The value of thermal capacity of a body depends upon the nature of the body and its mass.
When heat is given to a body and its temperature increases, the heat required to raise the temperature of the unit mass of a body through ${{1}^{0}}$C or 1 K is called specific heat capacity of the material of the body.
If Q heat changes the temperature of mass m by $\Delta $T.
Then specific heat is given as $c=\dfrac{Q}{m\Delta T}$.
We got the first difference in the definition of the two quantities.
The second difference is that heat capacity depends on the property of the material and mass of the body whereas specific heat capacity only depends on the property of the material.
The SI unit of heat capacity is $\dfrac{Joule}{Kelvin}$.
The SI unit of specific heat capacity is $\dfrac{Joule}{kg.Kelvin}$.

Note: Suppose Q amount of heat is given to a body of mass m and its temperature raises by $\Delta $T. Let the heat capacity of the body be C.
Then, $C=\dfrac{Q}{\Delta T}$ …… (1).
Let the specific heat capacity of the body be c.
Then, $c=\dfrac{Q}{m\Delta T}$ …… (2).
Divide (1) by (2).
We get,
$\dfrac{C}{c}=\dfrac{\dfrac{Q}{\Delta T}}{\dfrac{Q}{m\Delta T}}$
$\Rightarrow \dfrac{C}{c}=m\Rightarrow C=mc$.
Therefore, the heat capacity of a body is the mass of the body times its specific heat capacity.