Question

Heat capacity $\left(C_p\right)$ is an extensive property but specific heat $\left(c\right)$ is an intensive property. What will be the relation between $C_p$ and $c$ for $1$ mole of water?

Answer 1

• Heat capacity $\left(C_p\right)$ of a substance is the amount of heat energy required in order to raise its temperature by $1^{\circ }C$.

$C_p=\frac{q}{\Delta T}$ ………….$\left(1\right)$

• The specific heat is the amount of heat required to raise the temperature of $1g$ of substance by $1^{\circ }C$.

$C=\frac{q}{\Delta T\times m}$ ………….$\left(2\right)$

$1$ mole of water $=18g$

Hence, $m=18g$

On substituting value of m in equation $\left(2\right)$

$c=\frac{q}{\Delta T\times 18}$

Now, relating this equation with equation$\left(1\right)$,

$c=\frac{C_p}{18}$

Hence, $C_p=c\times 18$ (for $1$ mol of water)
Heat capacity $=18\times$ specific heat.