2.10Elementary thermodynamics

Thermodynamics is the study of heat, temperature, and their related e ects in physical systems. As a subject, thermodynamics is quite complex and expansive, usually taught as a course in itself at universities. The coverage in this book is limited to some of the more elementary and immediately practical facets of thermodynamics rather than a comprehensive overview.

2.10.1Heat versus Temperature

Most people use the words heat and temperature interchangeably. This is unfortunate for every student of thermodynamics, because it means they must first deconstruct this false conception and replace it with one more scientifically accurate before any progress may be made. While “heat” and “temperature” are related concepts, they are not identical.

When people say something is “hot,” what they really mean is that the object has a high temperature. Temperature is a direct function of random molecular motion within an object or a fluid sample. This is usually easiest to visualize for a gas, where unattached molecules have great freedom to vibrate, collide, and otherwise move about. The molecules of a substance at high temperature are moving more vigorously (higher velocity) than the molecules of the same substance at low temperature.

Heat, by contrast, is an expression of thermal energy transfer. By placing a pot of water over a fire, we are adding heat to that pot (transferring thermal energy to the water), the e ect of which is to raise its temperature (making the water molecules’ motions more vigorous). If that same pot is taken away from the fire and allowed to cool, its loss of heat (transferring energy out of the water to the surrounding air) will result in its temperature lowering (the individual water molecules slowing down).

Heat gain or loss often results in temperature change, but not always. In some cases heat may be gained or lost with negligible temperature change – here, the gain or loss of heat manifests as physical changes to the substance other than temperature. One example of this is the boiling of water at constant pressure: no matter how much heat is transferred to the water, its temperature will remain constant at the boiling point (100 degrees Celsius at sea level) until all the water has boiled to vapor. The addition of thermal energy to the boiling water does not raise its temperature (i.e. make the molecules move faster), but rather goes into the work of disrupting inter-molecular bonds so that the liquid turns into vapor. Another example is the heating of chemical reactants in an endothermic (heat-absorbing) reaction: much of the thermal energy added to the chemical solution goes into the work of separating chemical bonds, resulting in molecular changes but not (necessarily) increased temperature.

Heat transfer can only happen, though, where there is a di erence of temperature between two objects. Thermal energy (heat) naturally flows from the “hotter” (higher-temperature) substance to the “colder” (lower-temperature) substance. To use the boiling water example, the only way to get heat transfer into the water is to subject the water to a hotter substance (e.g., a flame, or a hot electric heating element). If you understand temperature as being molecular motion within a substance, with a hotter object’s molecules vibrating more vigorously than a colder object’s molecules, this natural transfer of heat from hot to cold makes perfect sense: the molecular vibrations of the highertemperature object literally transfer to the molecules of the lower-temperature object. As those respective molecules touch each other, with fast-vibrating molecules colliding against slow-vibrating molecules, the inter-molecular collisions transfer energy away from the fast-vibrating molecules (so they aren’t vibrating as fast anymore) and toward the slow-moving molecules (so they begin to vibrate faster than before). It’s like a vibrating tuning fork touched to a non-vibrating tuning fork: the vibrating fork loses some of its vibration by transferring energy to the (formerly) quiet tuning fork.

Much more attention will be directed to the concepts of heat and temperature in subsequent subsections.

A table of melting and boiling points (at sea-level atmospheric pressure) for various substances appears in this table, labeled in these four di erent units of temperature measurement:

Note how degrees Celsius and Kelvin for each point on the table di er by a constant (o set) of 273.15, while each corresponding degree Fahrenheit and degree Rankine value di ers by 459.67 (note that many of the figures in this table are slightly rounded, so the o set might not be exactly that much). You might think of Kelvin as nothing more than the Celsius scale zero-shifted by 273.15 degrees, and likewise degrees Rankine as nothing more than the Fahrenheit scale zero-shifted by 459.67 degrees.

Note also how increments in temperature measured in degrees Fahrenheit are the same as increments of temperature measured in degrees Rankine. The same is true for degrees Celsius and Kelvin. The di erence between the melting point of ammonia (−77.7 degrees C) and the melting point of water (0 degrees C) is the same di erence as that between the melting points of ammonia and water expressed in Kelvin: 195.45 and 273.15, respectively. Either way, the di erence in temperature between these two substances’ melting points is 77.7 degrees (C or K). This is useful to know when dealing with temperature changes over time, or temperature di erences between points in a system – if an equation asks for a temperature di erence (ΔT ) in Kelvin, it is the same value as the temperature di erence expressed in Celsius. Likewise, a T expressed in degrees Rankine is identical to a T expressed in degrees Fahrenheit. This is analogous to di erences between two fluid pressures expressed in PSIG versus PSIA: the di erential pressure value (PSID) will be the same.

Most people are familiar with the Fahrenheit and Celsius temperature scales used to express temperature in common applications, but the absolute scales of Rankine and Kelvin have special significance and purpose in scientific endeavors. The fact that Rankine and Kelvin are absolute scales in the same manner that atmospheres and torr are units of absolute pressure measurement makes them uniquely suited for expressing temperature (molecular motion) in relation to the absence of thermal energy. Certain scientific laws such as the Ideal Gas Law and the Stefan-Boltzmann Law relate other physical quantities to absolute temperature, and so require the use of these absolute units of measurement.