Heat Capacity

The third law of thermodynamics states that the entropy of a system will approach a constant value as the temperature approaches absolute zero, such as the entropy is zero at absolute zero (which is -273 degrees Celsius or 0 degrees Kelvin). At absolute zero, the entropy of a pure crystalline substance is zero.

HEAT CAPACITY

The heat capacity or thermal capacity is a measurable number that is equal to the ratio of heat added to or removed from a given object to the resulting temperature change. The unit for this is joules per Kelvin (which is the SI unit). The specific heat of an object is the amount of heat necessary to raise an object of one kilogram of mass up 1-degree Kelvin.

Heat capacity by itself is considered an “extensive property” of matter because it is directly proportional to the size of the system. If expressing the phenomenon as an “intensive property”, the heat capacity is also divided by the amount of the substance (the mass, number of molecules, or volume). The term “specific” is an intensive property of a substance because it refers to a certain mass of a substance. The specific heat capacity in SI units is Joules per kilogram per degree Kelvin. Water, for example, has a heat capacity of 4.186 joules per gram per degree Celsius.

In chemistry, an intensive property of heat is specified relative to a mole of a substance, such as the molar heat capacity, which has the units of joules per mole per degree Celsius. In engineering and other scientific circles, there is the volumetric heat capacity, which is the heat capacity per unit of volume, giving it the units of Joules per cubic meter Kelvin. Calories are sometimes used in place of joules in certain industries. The specific heat capacity in this system is one calorie per kilogram per degree Celsius.

There are different ways to measure the heat capacity. It involves adding a known amount of heat to a substance and measuring the change in temperature. This only really works well in the measurement of solids. Gases and liquids are held to a constant pressure or constant volume—most likely constant volume because there is energy necessary in gases to hold them to a constant pressure that interferes with the specific

heat capacity. The specific heat capacity of certain substances will vary according to the temperature.

Measuring the specific heat at constant volume can be difficult for liquids and solids. Small changes in temperature will require a very rigid and strong containing vessel because large pressures are required to keep the volume of a solid or liquid constant as heat is added to the system. For this reason, it is better to keep the pressure constant, allowing material to expand or contract, in order to measure the heat capacity of the substance.

Because the heat capacity is in Joules/kelvin, the heat capacity of a substance at absolute zero would be infinite, which violates the third law of thermodynamics. For this reason, the heat capacity at absolute zero is said to be zero. This involves a simple calculus term in which the heat capacity is calculated as the limit of heat capacity as the change in temperature approaches zero.

Molecules have many internal vibrations with potential energy stored in the different degrees of freedom of the molecules in a given sample. The more internal degrees of freedom of a substance, the greater is its specific heat capacity at high enough temperatures to overcome the quantum effects of the molecule, which are greater effects near absolute zero. Each independent degree of freedom allows for greater storage of thermal energy.

So, what are degrees of freedom? There is the free 3-dimensional ability of substances to move in space when heat (or any type of energy) is added to the system. This is called translational kinetic energy. There is also rotational kinetic energy of a substance (mainly an atom or molecule). There are only three degrees of translational kinetic energy, corresponding to three dimensions (x, y, and z dimensions). Rotational energy depends on the size and degree of inertia of an atom (which is small for a small single atom but bigger for molecules and larger atoms). Molecules are polyatomic and will have rotational energy. This will allow these types of substances to have a fourth degree of freedom. Finally, there are internal vibrational degrees of freedom of an atom.

While there are three degrees of translational freedom, there are also three rotational degrees of freedom, which also involves the three degrees in three-dimensional space.