# Adiabatic Work

See: https://www.youtube.com/watch?v=bvW-Mtv939Y for a video presentation.
The adiabatic condition for a piston is “well insulated” or “very fast” such that no heat is transferred out of the system during expansion or compression. In that case, dq=0. No input or output of heat. That means that there will be a change in temperature. Heat doesn’t flow from or to an adiabat, so it stays with the system and is manifested by a change in temperature.
Gamma is the ratio of Cp/Cv. It is always greater than 1. Gamma can be changed in the algebra window. The sheet defaults to a monatomic gas with gamma = 5/3.
The blue adiabatic PV curve comes from P=k/V^gamma. The constant, k, can be computed from any known pressure and volume and is usually obtained from P0 and V0. Vinitial and V0 are the same volume with different names. Vfinal is the second volume that is achieved after expansion or compression.
Derivation of this equation can be found online. [See for example: http://ocw.mit.edu/courses/chemistry/5-60-thermodynamics-kinetics-spring-2008/video-lectures/lecture-5-adiabatic-changes/
T0 is the initial temperature. All temperatures are in Kelvin.
All calculations should be performed with Pascals and cubic meters. This is critical, since we are raising volume to a power. The worksheet displays Pascals (y-axis) and Liter (x-axis). Liters are not strict SI units and while the worksheet may give the correct answers, it does so only at the expense of introducing stray factors of 1000 here and there as needed. Hand calculations will work if using strict SI units.
Two isothermal curves are also shown. These are graphed in order to answer questions such as “Would it take more or less energy to perform an adiabatic compression or an isothermal compression?”. You could integrate the Iso1 curve from Vi to Vf and find out.

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