Basic Thermodynamics ~ J. Pohl © | www.askdrthermo.com |
Time is a grand abstract. Time has to do with every system but it is not a system property. We make time quantitative on a relative scale. It marks and measures sequences of events.. which occured first, second, next and so on. Time does not participate in events, it is an observer. Thermodynamics uses special aspects of matter and of time to describe physical events of that matter.
- Batch or Increment Event:
Some physical events exhibit the distinct time aspect we describe as, "start and stop". Thermodynamics calls such events, batch or increment events. To split a log with an ax, open a bottle or cook an egg, are examples. A batch event initiates with a distinct beginning as when the falling axe impacts the log, the in place bottle opener is lifted, when the egg is broken into the pan. The batch event ends distinctly... the log falls in two pieces, the cap pops free of the bottle, or when the egg is moved from the pan to the plate. Systems of increment or batch type events generally have some physical characteristic, some manner of catalyst or trigger, that, upon actuation, initiates the event which stops upon its completion.
- Continuing Event: Ageing is an example. We age. Since time continues, all of physical reality experiences a continuing event. More pointedly, a system that receives energy steadily while energy in an equal amount passes from it, that is, having no system energy change, that system experiences a continuing event.
- Null Event:
The simplest event is a non-event, meaning no change. Permanence or the term null event; is used by some. The concrete and steel structures of hydro-electric dams and bridges were designed with the intention of no event. To have no change whatsoever, forever... to last forever. Spent nuclear fuels (in their trash containers) will change negligibly, will be lethal to us for a few million years. Theri degradation is one event, their lethality another, altogether. Everything changes, of course. Time means change. Of course there is no permanance. That would mean denial of reality - time.
- Differential Event: Calculus casts change in its smallest perspective. The differential is mathematical. The differential anything exists only on paper and in the mind. To apply to anything real, the differential must be integrated. The differential event is an invention of Newton. This is the very special change of a system in the limit (with vanishing time) as to be so small as to be no change but yet a change. The notation d; written before a variable (e.g., dX) means the very slightest change of X, or the last of diminishing changes of X before the change is zero, meaning no change. The limit and differential is a powerful idea of mathematics
Time-Related Notations
TIME and TIME-RELATED NOTATIONS: Time is a human perception and also a dimension of our sciences. Time is measurable; our clocks measure the lengths of our lives as we live. Our clocks tell us where we are in the day, calenders place the day in a larger time frame - the year. We use the idea of time scientifically, to explain the past or predict the future. Some special notations for thermodynamics follow:
- t : This symbol means time in the arbitrary sense. The letter, "t," is a variable and is often written (as would be an X) on an axis designating time.
- t < 0 : This notation is used to means "all times prior to an event."
- t = 0 : This notation is ambiguous. Time being "0" (zero) is the beginning of an epoch but has the epoch commenced at tome equal to "0" ? (read below)
- t = 0+ : This notation of an epoch or era is clear. The notation means to set a clock at time zero BUT running. Zero is the "initial time," associated with initial conditions of the system. The superscript, + emphasizes event has commenced, that timing (the clock that measures the duration of the event) has commenced.
- t* : nbsp;Often in an event, the conditions of some instance in time... an instance but not any specific instance are meant. Calculus, for example (by Newton and Leibnitz) defines the position with respect to time "at an instance in time" that is at t* :.divided by change in time Δ t ... in the limit that Δ t becomes "vanishingly small.
- tfin : This time denotes the completion, the termination or ending time of an event.
- t1, t2... : Arbitrary time (t), when subscripted, means a specific instance at time, generally greater than "0+" and less than tfin.
- Δt : This notation is called "an increment in time." It is an inspecific, finite amoune of time. A common meaning is: Δt = t2 - t1 and obviously t1 + Δt = t2
- Initiation of event. Time marks the initiation of an event, that specific, t*, at the dtart of an event is notated, "t = 0+ " At t* = 0, nothing is happening but just a nano-seconds later, t = 0+, the event is under way.
- Increment of Time is a duration or the time between two instances, It is written Δt, meaning the later time minus the initial or t2 - t1. Other subscripting used is "tstart, or "t1" with "t2" or "tfinal."
- Differential Time is an idea from calculus.Calculus uses the notation, "dt", to mean a time difference in the limit that it vanishes. "dt" is differential time. The duration of "dt" is zero seconds.
The above examples and explanations have refreshed our memories of some aspects of physics. Math, vectors and calculus are the tools of thermodynamic analysis. Here even simple problems, with obvious answers, will be posed mathematically for analysis. The purpose is solve the easy problems correctly so as to learn a method for more difficult problems.