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.