Measuring heat

When something absorbs heat, it gets hotter and when it loses heat it cools down. There must, therefore, be a relationship between the change in temperature and the amount of heat transferred.

It turns out that the size of the temperature change when something absorbs or gives off heat depends on three factors:

• the amount of heat transferred, 
• the identity of the object giving off or taking in hea
• the mass of the object 

Let's think about each of those separately.

Amount of heat: The more heat something absorbs, the hotter it gets. This should not be a surprise. A pot of water on the stove continues to get hotter the longer it sits over the fire. A drink gets colder the longer you leave it in the refrigerator.

Identity: Different types of materials absorb heat differently. This is the idea behind the specific heat (or specific heat capacity) of different materials.

Mass: When heat is absorbed by an object, that heat can be spread around the entire object. For instance, the heat from the stove doesn’t warm only the water on the bottom of the pot. Instead, that heat is transferred and shared throughout all of the water. As a result, the more water there is in the pot, the less heat each molecule of water gets and the smaller temperature change will occur. In simple terms, the larger the object, the more heat is needed to make it hotter.

The Math 

There is a mathematical formula that puts all of these ideas together.

In this formula, q is the symbol for heat, m is the mass of the object being heated, c is the specific heat of the object and ΔT is the change in temperature.

This formula allows us to do many different types of problems.

It is important to note that ΔT has a sign associated with it. When the temperature goes down, ΔT is negative and when the temperature rises, ΔT is positive.

In order to make the math give us those signs, ΔT is always calculated

ΔT = T_final-T_initial.

It is important to recognize that as a result of this, heat also has a sign associated with it as well. If ΔT is negative, then q will be negative as well. If the ΔT is positive, then q will be positive.

Take a moment to consider that mathematical consequence.

We know that ΔT is positive when the temperature is rising (when T_final is higher than T_initial). In that case, q is also positive. Remembering that temperature rises when something absorbs heat, we say that q is positive if something absorbs heat.

We also generalize that definition saying that anytime q is positive heat is being absorbed. This (heat being absorbed) is called an endothermic process.

ΔT (and therefore q) is negative when the temperature is falling (when T_initial is higher than T_final). Since temperature falls when something loses heat, we say that q is negative when something loses heat. Again, we generalize this idea and say that anytime q is negative heat is being lost. Losing heat is called an exothermic process.