Measuring Entropy

One useful way of measuring entropy is by the following equation:

where S represents entropy, DS represents the change in entropy, q represents heat transfer, and T is the temperature. Using this equation it is possible to measure entropy changes using a calorimeter. The units of entropy are J/K.

The temperature in this equation must be measured on the absolute, or Kelvin temperature scale. On this scale, zero is the theoretically lowest possible temperature that any substance can reach. At absolute 0 (0 K), all atomic motion ceases and the disorder in a substance is zero.

How are the Kelvin and Celsius
temperature scales related?

The absolute entropy of any substance can be calculated using equation (1) in the following way. Imagine cooling the substance to absolute zero and forming a perfect crystal (no holes, all the atoms in their exact place in the crystal lattice). Since there is no disorder in this state, the entropy can be defined as zero. Now start introducing small amounts of heat and measuring the temperature change. Even though equation (1) only works when the temperature is constant, it is approximately correct when the temperature change is small. Then you can use equation (1) to calculate the entropy changes. Continue this process until you reach the temperature for which you want to know the entropy of a substance (25 ºC is a common temperature for reporting the entropy of a substance).

The Thermodynamics Table lists the entropies of some substances at 25 ºC. Note that there are values listed for elements, unlike DH_fº values for elements. The reason is that the entropies listed are absolute, rather than relative to some arbitrary standard like enthalpy. This is because we know that the substance has zero entropy as a perfect crystal at 0 K; there is no comparable zero for enthalpy. The fact that a perfect crystal of a substance at 0 K has zero entropy is sometimes called the Third Law of Thermodynamics.

Measuring Entropy