Quantity of heat and the resulting temperature change (14-20)

Review

Experiment shows that in most circumstances the flow of heat into or out of an object changes the object’s temperature. (The exception is when the object undergoes a phase change such as from solid to liquid, liquid to solid, liquid to gas, or gas to liquid. In the next section we’ll discuss what happens in a phase change.) If the quantity of heat $Q$ that flows into an object is rela­ tively small, the resulting temperature change $\Delta{T}$ turns out to be directly proportional to $Q$ and inversely proportional to the mass $m$ of the object. In other words, the greater the quantity of heat $Q$ that flows into an object, the more its temperature changes; the more massive the object and so the more material that makes up the object, the smaller the temperature change for a given quantity of heat $Q$. (The same quantity of heat that will cook a single meatball will cause hardly any temperature change in a pot roast.) We can write this relationship as

$\Delta{T} = (\mathrm{constant}) \times \frac{\mathrm{Q}}{m}$

The constant in this equation depends on the substance of which the object is made. It’s conventional to express this equation as

The quantity $c$ is called the specific heat of the material that makes up the object. Its units are joules per kilogram per Kelvin ($\mathrm{J}/(\mathrm{kg}\cdot\mathrm{K)}$ or $\mathrm{J} \cdot \mathrm{kg}^{-1} \cdot \mathrm{K}^{-1})$ For example, the value of $c$ for aluminum is 910 $\mathrm{J}/(\mathrm{kg} \cdot \mathrm{K})$; this means that 910 J of heat must flow into a 1-­kg block of aluminum to raise its temperature by 1 K (or, equivalently, $1^\circ\mathrm{C}$).