Entropy

Draft Text Only – Readers’ suggestions and inputs are welcome

When a car or locomotive runs or brakes, we say that the heat escaping from it is “lost”. The Second Law of Thermodynamics explains this by saying that “energy will tend to dissipate from a hot or high energy body to a cold or low energy sink”. However since the First Law states that “energy cannot be created or destroyed”, then the “lost energy cannot simply disappear.

The concept of entropy was invented to account for this anomaly. This “waste heat” (or waste energy) dissipates into the atmosphere which acts as a heat sink, absorbing the energy without measurable increase in temperature. In so doing, the absorbed heat or energy effectively becomes “useless” (or wasted) to the extent that it cannot be put to further practical use.

Merriam Webster’s on-line dictionary offers three reasonably understandable definitions of entropy as follows:

a measure of the unavailable energy in a closed thermodynamic system that is also usually considered to be a measure of the system’s disorder, that is a property of the system’s state, and that varies directly with any reversible change in heat in the system and inversely with the temperature of the system; broadly : the degree of disorder or uncertainty in a system;
the degradation of the matter and energy in the universe to an ultimate state of inert uniformity;
a process of degradation or running down or a trend to disorder.

A better defintion comes from mathpages.com which offers the following: “The property that we call entropy is a measure of the uniformity of the distribution of energy”. It goes on to state that the entropy of a system equals the sum of the entropies of its component parts.

In simplistic terms, entropy can be thought of as a means of quantifying degraded or “useless” energy. The flame in a locomotive firebox contains a high concentration of energy (enthalpy) and a relatively low entropy, while the (lower temperature) steam in the boiler has a lower enthalpy and greater entropy. Exhaust steam leaving the chimney has an even lower enthalpy and higher entropy.

In fact, contrary to Merriam Webster’s definition, entropy is not a measure of energy. This may be deduced by the fact that by definition, the entropy of a closed system (e.g. the universe) gradually increases over time and is therefore not conserved. Entropy is in fact defined in units of energy per unit of temperature, as per the equation S₁ – S₂ = δQ/T where δQ represents a (small) amount of heat transfer to or from a body, T is its temperature and S₁ and S₂ its entropy before and after the energy transfer. The equation can be written dS = dQ/T giving entropy in units of energy per unit of temperature.

Specific entropy is the entropy of a system (usually a gas) divided by its mass, or in other words its entropy per kg in units of Joules per kg per ^oK.

In practical steam locomotive terms, values of specific entropy are usually found by looking them up in a set of steam tables or deriving them from a steam table program.

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