# Why is specific heat an intensive property?

Aug 11, 2018

Because of the definition of intensive .

#### Explanation:

An intensive property is one which does not change if you increase or decrease the amount of the matter present. Color is such a property. Black paint is black whether you have a lot of it or a small amount of it.

The heat added to an object is related to the resulting temperature change and its mass by the formula

$Q = m \cdot c \cdot \Delta T$

Specific heat is the character $c$ in that formula. Solving for $c$,

$c = \frac{Q}{m \cdot \Delta T}$

Assume you have 2 samples of copper, one 2X the mass of the other. You control the amount of heat applied, $Q$, and determine the temperature change, $\Delta T$, that results for both. If you give identical amount of heat to each, the temperature change of the lighter one will be double the change of the heavier one. And if you calculate $c$, you will get (or should get) the same result for both.

I hope this helps,
Steve