Definition of Heat Capacity

Heat capacity is an important property of materials that must be considered in engineering devices, planning a scientific experiment and keeping your lunch cold. There are three main types of heat capacity, the understanding of which will expand your ability to take advantage of this property of matter.

Definition

A material's heat capacity is a measure of how much energy must be exchanged between an object and its environment to produce a change in temperature. In other words, it is a measure of an object's "capacity" to hold "heat." Materials with high heat capacities, such as water, require large amounts of energy to produce a small temperature change.

Significance

Gardeners shield their tomatoes with water-walls, and during the Middle Ages, a lady-in-waiting put hot rocks into her master's bed. Both practices rely on the ability of water and stone to hold heat very well, a property owing to the fact that they have a high heat capacity.

Heat capacity is used for much more than saving tomatoes or keeping feet warm. It is an essential parameter considered in many fields of engineering from architecture to aerodynamics.

Types of Heat Capacity

The general term "heat capacity" includes three more specific, often confused, terms. These are molar heat capacity, specific heat and just heat capacity.

Molar Heat Capacity and Specific Heat

A substance's molar specific heat capacity is the amount of energy required to raise one mole of that substance 1 degree Celsius. A mole specifies a number of objects, as does a dozen, except a mole equals 6.02 x 10^23 objects instead of 12. Because of the way the mole is defined, one mole of a substance is equal to that substance's atomic or molecular mass in grams.

The more general term "specific heat" usually refers to the amount of energy required to raise a certain mass of material, usually a kilogram, 1 degree Celsius. This is probably the most common use of the term "heat capacity."

Both molar heat capacity and specific heat are intrinsic properties of a substance; that is, they are independent of the amount of material you have on hand.

Heat Capacity

An object's heat capacity, C, is the product of its specific heat capacity (the amount of heat required to raise 1 kg of the material 1 degree C) and its mass in kg. Heat capacity is an extensive property of a substance. That is, its value depends on how much substance you have. For example, the heat capacity of a 20 oz. soda is exactly double that of a 10 oz. soda.

Mathematical Definition and Theory

Mathematically, heat capacity is defined as the first order partial derivative of the change in heat of an object with respect to the object's change in temperature, all else being held constant. The root of what determines a substance's heat capacity is a course in statistical thermodynamics. However, there is a general rule: the larger and more free molecules are, the greater their heat capacity will be. In other words, the more degrees of freedom the atoms or molecules making up a substance have, the greater the heat capacity will be.

Examples of Heat Capacity in Use

Metals tend to have very low heat capacities compared to nonmetals. For example, 1 kg of copper has a heat capacity of 394 Joules per Celsius, while 1 kg of marble has a heat capacity of 880. Thus, stone can hold much more heat than metal.

The definition of a calorie is based on the heat capacity of water. A dietary Calorie (note the capital C) is the amount of heat required to raise the temperature of 1 kg of water 1 degree. Therefore, if all of the Calories in a Twinkie (150) went toward heating 1 liter of water at room temperature, say at 22 degrees Celsius, then the Twinkie would have enough energy to raise the temperature of the water to boiling and then some.

Fortunately for us, our bodies burn Twinkies in a controlled, slow release sort of way.