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NotesforChapter19 - Physics 4C Chapter 19 Notes Page 1 of...

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Physics 4C Chapter 19 Notes Page 1 of 12 Quick note before the notes… if you find any typos or anything that is confusing, please let me know. All of this makes perfect sense to me when it’s going from my brain to my fingers, but the only thing that matters is how it reads to you. If any part is too confusing, I may be able to edit the notes and repost. Thanks! Notes for Chapter 19 Work by an ideal gas Thermodynamic processes of an ideal gas pV diagrams First Law of Thermodynamics Molar heat capacity of an ideal gas Adiabatic process Work done by an ideal gas In lecture we established that the work done by an ideal gas , for any process, is: W = p dV We established this by simply using the definition of work, Force times Displacement, and adapting it to the parameters of our gas. The integral is necessary because, in general, the pressure (and therefore the force the gas applies) changes as the volume changes. Important note: this expression is for the work done by the gas, which is the negative of the work done on the gas. We will use work done by the gas for chapters 19 and 20. Your homework problems may ask for the work done on the gas. To find this, simply take the negative of the work done by the gas. Thermodynamic processes of an ideal gas A “state” of a gas is described by the unique combination of its pressure, volume and temperature. A “thermodynamic process” is simply the action of a gas changing its state; that is, it changes its pressure, volume and/or temperature and after is at a new “state”. Remember that the ideal gas law: p V = n R T is applicable for any problem in chapters 17 and 18 which involves a gas. We now use the ideal gas law to recognize that, in general, the pressure, volume and temperature of a gas can all change during a “thermodynamic process”. However, we can define three “special processes”: o Constant volume (“isochoric”, only pressure and temperature change)
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Physics 4C Chapter 19 Notes Page 2 of 12 o Constant pressure (“isobaric”, only volume and temperature change) o Constant temperature (“isothermal”, only volume and pressure change) Using the above definition for work, we can establish expressions for the work done by the gas during each of these processes. Constant volume: volume does not change, so work is zero. Constant pressure: W = p dV = p dV = W = p ( V f - V i ) (constant pressure or “isobaric” process) (note: p can be “factored out” because it is constant) Constant temperature: W = p dV = ( n R T / V) dV = n R T ( 1 / V) dV = W = n R T ln ( V f / V i ) (constant temperature or “isothermal” process) Quick and important note about work done by an ideal gas : if the volume of the gas increases, the work done by the gas is positive; if the volume decreases, the work done by the gas is negative.
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