Subsection 10.3.1 Specific Heat Capacity
Heat absorbing capacity of a material is known as specific heat capacity. Suppose we have two marbles at room temperature \(T_{o}=25^{o}C\text{,}\) one has mass 1 kg and another has mass 2 kg. If we want to heat them to \(100^{o}C\text{,}\) then from our experience we know that 2 kg marble will take longer than 1 kg marble to reach at the same temperature. Hence, the amount of heat (Q) put into the material is directly proportional to the mass (m) of the material. That is,
\begin{equation*}
Q \propto m
\end{equation*}
Now suppose both of our marbles has a mass of 1 kg each and we want to heat one of them for \(T_{1}= 100^{o}C\) and another for temperature \(T_{2}= 200^{o}C.\) We can again tell that the marble which has to be heated for \(200^{o}C\) will take longer than the other. That is,
\begin{equation*}
Q \propto \Delta T
\end{equation*}
where \(\Delta T = T_{f}-T_{o}\text{.}\) For marble of mass 1 kg, \(\Delta T = 100-25 =75^{o}C\) and for the marble of mass 2 kg \(\Delta T = 200-25 =175^{o}C.\) By combining these two expressions, we have -
\begin{equation*}
Q\propto m\Delta T
\end{equation*}
\begin{equation*}
\therefore\quad Q = mc\Delta T
\end{equation*}
where \(c\) is a proportionality constant and is called specific heat capacity of the material. It is the properties of a material. Different materials have different specific heat capacities and hence they absorb or release heat differently.
\begin{equation*}
c=\frac{Q}{m\Delta T}
\end{equation*}
If m=1 kg, \(\Delta T= 1^{o}C\text{,}\) then \(c=Q\text{,}\) i.e., specific heat capacity of a material is the amount of heat added into or taken out from the material of unit mass to the unit degree rise or fall of temperature. In SI system, unit of \(c\) is \(J/kg/^{o}C\text{.}\) In heat and thermodynamics, we normally measure heat in calorie unit but other physical quantities in SI unit. Hence the mixture of systems of unit can be seen in this chapter. In cgs system, unit of specific heat capacity of water is \(1\,cal/g/^{o}C.\) The capacity of a material to absorb heat per degree rise of temperature is called heat capacity. It is defined as \(C=mc\text{.}\) The amount of heat required to raise the temperature of one mole of a substance by one degree (Celsius or Kelvin) is known as molar (specific) heat capacity.
1
\(1 \,cal = 4.186 \,J.\)
