02.01 Expansion/Contraction Work

Closed System Energy Balance: Ideal Gas Expansion (uakron.edu, 9min) An ideal gas is on the left side of a frictionless piston that expands to produce work energy. Beginning with the work energy of expansion and contraction, then contemplating the manners in which other forms of energy could impact this closed system, a checklist is developed for analyzing all the ways that energy can change in the system. This checklist is known as the energy balance, and in this particular case, for a closed system. This system forms the basis for three sample calculations (18min): (1) Adiabatic, reversible expansion from 1000C, 100 bars, and 0.1 L to 0.6L. (2) Isothermal, reversible expansion from 1000C, 100 bars, and 0.1 L to 0.6L. (3) Adiabatic, irreversible expansion from 1000C, 100 bars, and 0.1 L to 0.6L against a perfect vacuum. Calculate the temperature, pressure, work and change in internal energy at the final conditions. The gas can be assumed as pure air. NOTE: Case (1) leads to a very important equation that should be memorized ASAP! Quick answers to common questions (UA, 12min) illustrate easy ideal gas calculations.
Comprehension Questions:
1. Estimate the number of moles in the system. 
2. Compute the total work (J) for each case.
3. If all six of the cylinders like Case (1) are firing at the rate of 2500 times per minute, what would be the horsepower of such an engine?

Vocabulary in Sections 2.1-2.3: Forms of "Work." (uakron.edu, 11 min) Making cookies is hard work. In discussing work, we develop several shorthand terms to refer to specific common situations: expansion-contraction work, shaft work, flow work, stirring work, "lost" work. These terms comprise the headings of sections 2.1-2.3, but it is convenient to discuss them all at once. The important thing to remember is that work is really just force times distance, pure and simple. The shorthand terms are not intended to complicate the discussion, but to expedite the analysis of the energy balance. Developing some familiarity with the terms related to common daily experiences may help you to assimilate this new vocabulary. Sample calculations (13min) illustrate a remarkable difference when one is faced with gas compression vs. liquid pump work. 

Comprehension Questions:
1. How is "expansion-contraction" work related to force times distance?
2. What is the expression for "flow" work? Explain how it relates to force times distance for fluid flowing in a pipe.
3. What expression can we use for calculating "shaft" work, as in a pump or turbine? What is the technique of calculus to which it is related?