Q.Heat capacity (Cp) is an extensive property but specific heat

Concept: Extensive properties scale with amount; intensive properties do not. Specific heat is heat capacity per unit mass.

For any substance, the molar heat capacity $C_p$ (extensive, in $\text{J mol}^{-1} \text{K}^{-1}$) relates to specific heat $c$ (intensive, in $\text{J g}^{-1} \text{K}^{-1}$) through the molar mass $M$:

For water, $M = 18 \, \text{g mol}^{-1}$ and the specific heat is approximately $c = 4.18 \, \text{J g}^{-1} \text{K}^{-1}$. …

The distinction between extensive and intensive properties is central here. An extensive property scales with the amount of substance—double the water, double the heat capacity. An intensive property stays constant regardless of how much you have—the specific heat of water is the same whether you hold a drop or a lake.

Heat capacity $C_p$ tells you how much heat energy is required to raise the temperature of the entire sample by one degree. If you have more substance, you need more heat, so $C_p$ grows with the amount.

Specific heat $c$, on the other hand, is defined per unit mass. It answers: how much heat does one gram need? This ratio doesn't change when you add more grams—it's a material property.

The bridge between them is simply the mass of the sample:

where $m$ is the mass in grams and $c$ is in $\text{J g}^{-1} \text{K}^{-1}$.

For exactly one mole of water, the mass is the molar mass $M$:

1. Identify the mass of 1 mol of water.

   Water is H₂O, so $M = 2(1) + 16 = 18 \, \text{g mol}^{-1}$.

2. Substitute into the relation. …