Heat capacity and specific heat

Heating a body by $1\,°$C requires a certain amount of energy, which we call heat capacity $C$ (unit $\text{J/K}$). Heat capacity, however, depends both on the material and on how much material there is: doubling the mass doubles the energy required. It is therefore useful to separate the two effects by writing

$C = m\,c$

where $c$ is the specific heat (unit $\text{J/(kg K)}$), a property of the material rather than of the particular quantity. The specific heat tells us how many joules are needed to raise the temperature of one kilogram of substance by one degree.

Principle — Fundamental equation of calorimetry

The heat $Q$ exchanged by a body of mass $m$ and specific heat $c$ when its temperature changes by $\Delta T$ is $\ev{Q = m\,c\,\Delta T}$ with $Q > 0$ if the body absorbs heat (temperature rises) and $Q < 0$ if it releases heat.

Since only the difference $\Delta T$ appears in the formula, it makes no difference whether it is expressed in $°$C or in K. Specific heat values vary by almost an order of magnitude between common substances:

Substance	$c$ (J/(kg·K))
Liquid water	4186
Ice	2090
Water vapour	2010
Aluminium	897
Copper	385
Iron	452
Sand (dry)	~800
Air (20 °C, const. p)	1005

Water and the coastal climate

Water has the highest specific heat of any common substance, $4186$ J/(kg·K), almost an order of magnitude above nearly all other materials. It therefore takes a huge amount of energy to heat it, and it releases just as much on cooling: this is why the sea acts as a thermal flywheel and moderates the climate of coastlines, giving cooler summers and milder winters than inland areas.

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Topics: Thermology Concepts: Specific heat and heat capacity Skills: Calorimetric equation

Related exercises: Problem — Copper calorimeter · Worked exercise — Coffee and steam exchange · Problem — Four cups