# Expansion and Compression Boundary Work

x
The

#### work

done by the gas on the surroundings during the expansion is represented by the area under the curve of P versus V.
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### Ch 4, Lesson A, Page 11 - Expansion and Compression Boundary Work

• We conclude that the area under the process path, between the initial and final states, is the amount of work done on the surroundings during the process.
• I hope it is clear to you that the PATH that the process follows from 1 to 2 can DRAMATICALLY change the area under the curve.
• The area could be zero if the path went DOWN to P=0 atm and then RIGHT to V2 and finally back up to P2.
• Or the area could be HUGE if the path went up to P=1000 atm and then RIGHT to V2 and finally DOWN to P2.
• But in any case, areas are always positive, right ?  So, how can work ever turn out to be negative ?
• Well, if we integrated from 2 to 1, dV would be negative and the integral would actually be the NEGATIVE of the area under the curve.
• So, although area cannot be negative, integrals can.  If you integrate in the positive V-direction, dV is positive and the integral is equal to the area under the curve.
• If you integrate in the negative V-direction, dV is negative and the integral is equal to the negative of the area under the curve.
• Do you understand ?  Just be careful with this !